Recent zbMATH articles in MSC 82https://zbmath.org/atom/cc/822021-11-25T18:46:10.358925ZWerkzeugNetworks beyond pairwise interactions: structure and dynamicshttps://zbmath.org/1472.051432021-11-25T18:46:10.358925Z"Battiston, Federico"https://zbmath.org/authors/?q=ai:battiston.federico"Cencetti, Giulia"https://zbmath.org/authors/?q=ai:cencetti.giulia"Iacopini, Iacopo"https://zbmath.org/authors/?q=ai:iacopini.iacopo"Latora, Vito"https://zbmath.org/authors/?q=ai:latora.vito"Lucas, Maxime"https://zbmath.org/authors/?q=ai:lucas.maxime"Patania, Alice"https://zbmath.org/authors/?q=ai:patania.alice"Young, Jean-Gabriel"https://zbmath.org/authors/?q=ai:young.jean-gabriel"Petri, Giovanni"https://zbmath.org/authors/?q=ai:petri.giovanniSummary: The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a variety of complex systems has been successfully described as networks whose interacting pairs of nodes are connected by links. Yet, from human communications to chemical reactions and ecological systems, interactions can often occur in groups of three or more nodes and cannot be described simply in terms of dyads. Until recently little attention has been devoted to the higher-order architecture of real complex systems. However, a mounting body of evidence is showing that taking the higher-order structure of these systems into account can enhance our modeling capacities and help us understand and predict their dynamical behavior. Here we present a complete overview of the emerging field of networks beyond pairwise interactions. We discuss how to represent higher-order interactions and introduce the different frameworks used to describe higher-order systems, highlighting the links between the existing concepts and representations. We review the measures designed to characterize the structure of these systems and the models proposed to generate synthetic structures, such as random and growing bipartite graphs, hypergraphs and simplicial complexes. We introduce the rapidly growing research on higher-order dynamical systems and dynamical topology, discussing the relations between higher-order interactions and collective behavior. We focus in particular on new emergent phenomena characterizing dynamical processes, such as diffusion, synchronization, spreading, social dynamics and games, when extended beyond pairwise interactions. We conclude with a summary of empirical applications, and an outlook on current modeling and conceptual frontiers.Endowing evolution algebras with properties of discrete structureshttps://zbmath.org/1472.170992021-11-25T18:46:10.358925Z"González-López, Rafael"https://zbmath.org/authors/?q=ai:gonzalez-lopez.rafael"Núñez, Juan"https://zbmath.org/authors/?q=ai:nunez-valdes.juanIn this paper, the authors delve into the basic properties characterizing the directed graph that is uniquely associated to an evolution algebra, and which was introduced in [\textit{J. P. Tian}, Evolution algebras and their applications. Berlin: Springer (2008; Zbl 1136.17001)]. These properties are conveniently translated to algebraic concepts and results concerning the evolution algebra under consideration. In particular, the authors focus on the adjacency of graphs, whose immediate translation into algebraic language enables them to introduce the concepts of adjacency, walk, trail, circuit, path and cycle of an evolution algebra. Also the notions of strongly and weakly connected evolution algebras are introduced as the algebraic equivalences of the same concepts in graph theory. It enables the authors to introduce the notions of distance, girth, circumference, eccentricity, center, radio, diameter and geodesic of an evolution algebra, together with the concepts of Eulerian and Hamiltonian evolution algebras. Some basic results on these topics are then described. The relationship among all of these notions and their analogous in graph theory are visually illustrated throughout the paper.Geometric functionals of fractal percolationhttps://zbmath.org/1472.280082021-11-25T18:46:10.358925Z"Klatt, Michael A."https://zbmath.org/authors/?q=ai:klatt.michael-andreas"Winter, Steffen"https://zbmath.org/authors/?q=ai:winter.steffenSummary: Fractal percolation exhibits a dramatic topological phase transition, changing abruptly from a dust-like set to a system-spanning cluster. The transition points are unknown and difficult to estimate. In many classical percolation models the percolation thresholds have been approximated well using additive geometric functionals, known as intrinsic volumes. Motivated by the question of whether a similar approach is possible for fractal models, we introduce corresponding geometric functionals for the fractal percolation process \(F\). They arise as limits of expected functionals of finite approximations of \(F\). We establish the existence of these limit functionals and obtain explicit formulas for them as well as for their finite approximations.Complex dynamics in a quasi-periodic plasma perturbations modelhttps://zbmath.org/1472.341482021-11-25T18:46:10.358925Z"Zhang, Xin"https://zbmath.org/authors/?q=ai:zhang.xin|zhang.xin.4|zhang.xin.1|zhang.xin.3"Yang, Shuangling"https://zbmath.org/authors/?q=ai:yang.shuanglingSummary: In this paper, the complex dynamics of a quasi-periodic plasma perturbations (QPP) model, which governs the interplay between a driver associated with pressure gradient and relaxation of instability due to magnetic field perturbations in Tokamaks, are studied. The model consists of three coupled ordinary differential equations (ODEs) and contains three parameters. This paper consists of three parts: (1) We study the stability and bifurcations of the QPP model, which gives the theoretical interpretation of various types of oscillations observed in [\textit{D. Constantinescu} et al., ``A low-dimensional model system for quasi-periodic plasma perturbations'', Phys. Plasmas 18, No. 6, Article ID 062307, 7 p. (2011; \url{doi:10.1063/1.3600209})]. In particular, assuming that there exists a finite time lag \(\tau\) between the plasma pressure gradient and the speed of the magnetic field, we also study the delay effect in the QPP model from the point of view of Hopf bifurcation. (2) We provide some numerical indices for identifying chaotic properties of the QPP system, which shows that the QPP model has chaotic behaviors for a wide range of parameters. Then we prove that the QPP model is not rationally integrable in an extended Liouville sense for almost all parameter values, which may help us distinguish values of parameters for which the QPP model is integrable. (3) To understand the asymptotic behavior of the orbits for the QPP model, we also provide a complete description of its dynamical behavior at infinity by the Poincaré compactification method. Our results show that the input power \(h\) and the relaxation of the instability \(\delta\) do not affect the global dynamics at infinity of the QPP model and the heat diffusion coefficient \(\eta\) just yield quantitative, but not qualitative changes for the global dynamics at infinity of the QPP model.Asymptotic behavior of density in the boundary-driven exclusion process on the Sierpinski gaskethttps://zbmath.org/1472.352082021-11-25T18:46:10.358925Z"Chen, Joe P."https://zbmath.org/authors/?q=ai:chen.joe-p-j|chen.joe-p"Gonçalves, Patrícia"https://zbmath.org/authors/?q=ai:goncalves.patricia-cSummary: We derive the macroscopic laws that govern the evolution of the density of particles in the exclusion process on the Sierpinski gasket in the presence of a variable speed boundary. We obtain, at the hydrodynamics level, the heat equation evolving on the Sierpinski gasket with either Dirichlet or Neumann boundary conditions, depending on whether the reservoirs are fast or slow. For a particular strength of the boundary dynamics we obtain linear Robin boundary conditions. As for the fluctuations, we prove that, when starting from the stationary measure, namely the product Bernoulli measure in the equilibrium setting, they are governed by Ornstein-Uhlenbeck processes with the respective boundary conditions.Existence of a nonequilibrium steady state for the nonlinear BGK equation on an intervalhttps://zbmath.org/1472.352652021-11-25T18:46:10.358925Z"Evans, Josephine"https://zbmath.org/authors/?q=ai:evans.josephine"Menegaki, Angeliki"https://zbmath.org/authors/?q=ai:menegaki.angelikiSummary: We show existence of a nonequilibrium steady state for the one-dimensional, nonlinear BGK model on an interval with diffusive boundary conditions. These boundary conditions represent the coupling of the system with two heat reservoirs at different temperatures. The result holds when the boundary temperatures at the two ends are away from the equilibrium case, as our analysis is not perturbative around the equilibrium. We employ a fixed point argument to reduce the study of the model with nonlinear collisional interactions to the linear BGK model.Enhanced diffusivity in perturbed senile reinforced random walk modelshttps://zbmath.org/1472.352912021-11-25T18:46:10.358925Z"Dinh, Thu"https://zbmath.org/authors/?q=ai:dinh.thu"Xin, Jack"https://zbmath.org/authors/?q=ai:xin.jack-xSummary: We consider diffusivity of random walks with transition probabilities depending on the number of consecutive traversals of the last traversed edge, the so called senile reinforced random walk (SeRW). In one dimension, the walk is known to be sub-diffusive with identity reinforcement function. We perturb the model by introducing a small probability \(\delta\) of escaping the last traversed edge at each step. The perturbed SeRW model is diffusive for any \(\delta>0\), with enhanced diffusivity \((\gg O(\delta^2))\) in the small \(\delta\) regime. We further study stochastically perturbed SeRW models by having the last edge escape probability of the form \(\delta\xi_n\) with \(\xi_n\)'s being independent random variables. Enhanced diffusivity in such models are logarithmically close to the so called residual diffusivity (positive in the zero \(\delta\) limit), with diffusivity between \(O(\frac{1}{|\log\delta|})\) and \(O(\frac{1}{\log |\log\delta|})\). Finally, we generalize our results to higher dimensions where the unperturbed model is already diffusive. The enhanced diffusivity can be as much as \(O(\log^{-2}\delta)\).Erratum to: ``Volume viscosity and internal energy relaxation: symmetrization and Chapman-Enskog expansion''https://zbmath.org/1472.352972021-11-25T18:46:10.358925Z"Giovangigli, Vincent"https://zbmath.org/authors/?q=ai:giovangigli.vincent"Yong, Wen-An"https://zbmath.org/authors/?q=ai:yong.wen-anErratum to the authors' paper [ibid. 8, No. 1, 79--116 (2015; Zbl 1310.35196)].Jarzynski equality for conditional stochastic workhttps://zbmath.org/1472.353202021-11-25T18:46:10.358925Z"Sone, Akira"https://zbmath.org/authors/?q=ai:sone.akira"Deffner, Sebastian"https://zbmath.org/authors/?q=ai:deffner.sebastianSummary: It has been established that the \textit{inclusive work} for classical, Hamiltonian dynamics is equivalent to the two-time energy measurement paradigm in isolated quantum systems. However, a plethora of other notions of quantum work has emerged, and thus the natural question arises whether any other quantum notion can provide motivation for purely classical considerations. In the present analysis, we propose the \textit{conditional stochastic work} for classical, Hamiltonian dynamics, which is inspired by the one-time measurement approach. This novel notion is built upon the change of expectation value of the energy conditioned on the initial energy surface. As main results, we obtain a generalized Jarzynski equality and a sharper maximum work theorem, which account for how non-adiabatic the process is. Our findings are illustrated with the parametric harmonic oscillator.Semiclassical evolution with low regularityhttps://zbmath.org/1472.353232021-11-25T18:46:10.358925Z"Golse, François"https://zbmath.org/authors/?q=ai:golse.francois"Paul, Thierry"https://zbmath.org/authors/?q=ai:paul.thierrySummary: We prove semiclassical estimates for the Schrödinger-von Neumann evolution with \(C^{1,1}\) potentials and density matrices whose square root have either Wigner functions with low regularity independent of the dimension, or matrix elements between Hermite functions having long range decay. The estimates are settled in different weak topologies and apply to initial density operators whose square root have Wigner functions 7 times differentiable, independently of the dimension. They also apply to the \(N\)-body quantum dynamics uniformly in \(N\) and to concentrating pure and mixed states without any regularity assumption. In an appendix, we finally estimate the dependence in the dimension of the constant appearing on the Calderón-Vaillancourt Theorem.Transport equations and perturbations of boundary conditionshttps://zbmath.org/1472.353282021-11-25T18:46:10.358925Z"Tyran-Kamińska, Marta"https://zbmath.org/authors/?q=ai:tyran-kaminska.martaSummary: We provide a new perturbation theorem for substochastic semigroups on abstract AL spaces extending Kato's perturbation theorem to nondensely defined operators. We show how it can be applied to piecewise deterministic Markov processes and transport equations with abstract boundary conditions. We give particular examples to illustrate our results.Growth of Sobolev norms for coupled lowest Landau level equationshttps://zbmath.org/1472.353632021-11-25T18:46:10.358925Z"Schwinte, Valentin"https://zbmath.org/authors/?q=ai:schwinte.valentin"Thomann, Laurent"https://zbmath.org/authors/?q=ai:thomann.laurentSummary: We study coupled systems of nonlinear lowest Landau level equations, for which we prove global existence results with polynomial bounds on the possible growth of Sobolev norms of the solutions. We also exhibit explicit unbounded trajectories, which show that these bounds are optimal.Weak solutions of the relativistic Vlasov-Maxwell system with external currentshttps://zbmath.org/1472.353722021-11-25T18:46:10.358925Z"Weber, Jörg"https://zbmath.org/authors/?q=ai:weber.jorgThe paper studies the Vlasov-Maxwell system and their weak solutions when the plasma is contained in a bounded domain \(\Omega\) while the electromagnetic fields are induced by external currents outside the container. Here, the main contribution is that boundary conditions on \(E\) and \(H\) fields is not set to perfect electric conductor (PEC) at the boundaries of container. This is much more difficult problem but makes it possible for interaction of the fields inside container with currents in the control coils.
The author uses a method similar to [\textit{Y. Guo}, Commun. Math. Phys. 154, No. 2, 245--263 (1993; Zbl 0787.35072)] to identity the proper sets of test functions and function spaces for particle densities as well as \(E\) and \(H\) fields. The first of main results of the article is about the existence of the weak solutions for such a Vlasov-Maxwell system. The second major outcome is the examination of the divergence equations and demonstration of the redundancy of the \(E\) field based on the proposed weak formulation.
The proposed weak formulation is used in a separate article by the same author [SIAM J. Math. Anal. 52, No. 3, 2895--2929 (2020; Zbl 1448.35499)] to find optimal external currents that control the plasma particles.Contractivity for Smoluchowski's coagulation equation with solvable kernelshttps://zbmath.org/1472.353812021-11-25T18:46:10.358925Z"Cañizo, José A."https://zbmath.org/authors/?q=ai:canizo.jose-alfredo"Lods, Bertrand"https://zbmath.org/authors/?q=ai:lods.bertrand"Throm, Sebastian"https://zbmath.org/authors/?q=ai:throm.sebastianSummary: We show that the Smoluchowski coagulation equation with the solvable kernels \(K(x,y)\) equal to 2, \(x+y\) or \(xy\) is contractive in suitable Laplace norms. In particular, this proves exponential convergence to a self-similar profile in these norms. These results are parallel to similar properties of Maxwell models for Boltzmann-type equation, and extend already existing results on exponential convergence to self-similarity for Smoluchowski's coagulation equation.PDE/statistical mechanics duality: relation between Guerra's interpolated \(p\)-spin ferromagnets and the Burgers hierarchyhttps://zbmath.org/1472.353822021-11-25T18:46:10.358925Z"Fachechi, Alberto"https://zbmath.org/authors/?q=ai:fachechi.albertoSummary: We examine the duality relating the equilibrium dynamics of the mean-field \(p\)-spin ferromagnets at finite size in the Guerra's interpolation scheme and the Burgers hierarchy. In particular, we prove that -- for fixed \(p\) -- the expectation value of the order parameter on the first side w.r.t. the generalized partition function satisfies the \(p-1\)-th element in the aforementioned class of nonlinear equations. In the light of this duality, we interpret the phase transitions in the thermodynamic limit of the statistical mechanics model with the development of shock waves in the PDE side. We also obtain the solutions for the \(p\)-spin ferromagnets at fixed \(N\), allowing us to easily generate specific solutions of the corresponding equation in the Burgers hierarchy. Finally, we obtain an effective description of the finite \(N\) equilibrium dynamics of the \(p=2\) model with some standard tools in PDE side.Mathematical modeling of a temperature-sensitive and tissue-mimicking gel matrix: solving the Flory-Huggins equation for an elastic ternary mixture systemhttps://zbmath.org/1472.353832021-11-25T18:46:10.358925Z"Sung, Baeckkyoung"https://zbmath.org/authors/?q=ai:sung.baeckkyoungSummary: Programmed to retain active responsivity to environmental stimuli, diverse types of synthetic gels have been attracting interests regarding various applications, such as elastomer biodevices. In a different approach, when the gels are made of tissue-derived biopolymers, they can act as an artificial extracellular matrix (ECM) for use as soft implants in medicine. To explore the physical properties of hydrogels in terms of statistical thermodynamics, the mean-field Flory-Huggins-Rehner theory has long been used with various analytical and numerical modifications. Here, we suggest a novel mathematical model on the phase transition of a biological hybrid gel that is sensitive to ambient temperature. To mimic acellular soft tissues, the ECM-like hydrogel is modeled as a network of biopolymers, such as type I collagen and gelatin, which are covalently crosslinked and swollen in aqueous solvents. Within the network, thermoresponsive synthetic polymer chains are doped by chemical conjugation. Based on the Flory-Huggins-Rehner framework, our analytical model phenomenologically illustrates a well-characterized volume phase behavior of engineered tissue mimics as a function of temperature by formulating the ternary mixing free energy of the polymer-solvent system and by generalizing the elastic free energy term. With this formalism, the decoupling of the Flory-Huggins interaction parameter between the thermoresponsive polymer and ECM biopolymer enables deriving a simple steady-state formula for the volume phase transition as a function of the structural and compositional parameters. We show that the doping ratio of thermoresponsive polymers and the Flory-Huggins interaction parameter between biopolymer and water affect the phase transition temperature of the ECM-like gels.Periodic particle arrangements using standing acoustic waveshttps://zbmath.org/1472.353842021-11-25T18:46:10.358925Z"Vasquez, Fernando Guevara"https://zbmath.org/authors/?q=ai:guevara-vasquez.fernando"Mauck, China"https://zbmath.org/authors/?q=ai:mauck.chinaSummary: We determine crystal-like materials that can be fabricated by using a standing acoustic wave to arrange small particles in a non-viscous liquid resin, which is cured afterwards to keep the particles in the desired locations. For identical spherical particles with the same physical properties and small compared to the wavelength, the locations where the particles are trapped correspond to the minima of an acoustic radiation potential which describes the net forces that a particle is subject to. We show that the global minima of spatially periodic acoustic radiation potentials can be predicted by the eigenspace of a small real symmetric matrix corresponding to its smallest eigenvalue. We relate symmetries of this eigenspace to particle arrangements composed of points, lines or planes. Since waves are used to generate the particle arrangements, the arrangement's periodicity is limited to certain Bravais lattice classes that we enumerate in two and three dimensions.Homogenization and diffusion approximation of the Vlasov-Poisson-Fokker-Planck system: a relative entropy approachhttps://zbmath.org/1472.353852021-11-25T18:46:10.358925Z"Addala, Lanoir"https://zbmath.org/authors/?q=ai:addala.lanoir"El Ghani, Najoua"https://zbmath.org/authors/?q=ai:el-ghani.najoua"Tayeb, Mohamed Lazhar"https://zbmath.org/authors/?q=ai:tayeb.mohamed-lazharSummary: We are concerned with the analysis of the approximation by diffusion and homogenization of a Vlasov-Poisson-Fokker-Planck system. Here we generalize the convergence result of the second author and \textit{N. Masmoudi} [Commun. Math. Sci. 8, No. 2, 463--479 (2010; Zbl 1193.35228)] where the same problem is treated without the oscillating electrostatic potential and we extend the one dimensional result of the third author [Ann. Henri Poincaré 17, No. 9, 2529--2553 (2016; Zbl 1456.82798)] to the case of several space dimensions. An averaging lemma and two scale convergence techniques are used to prove rigorously the convergence of the scaled Vlasov-Poisson-Fokker-Planck system to a homogenized Drift-Diffusion-Poisson system.Spectrum analysis for the Vlasov-Poisson-Boltzmann systemhttps://zbmath.org/1472.353862021-11-25T18:46:10.358925Z"Li, Hai-Liang"https://zbmath.org/authors/?q=ai:li.hailiang"Yang, Tong"https://zbmath.org/authors/?q=ai:yang.tong"Zhong, Mingying"https://zbmath.org/authors/?q=ai:zhong.mingyingSummary: By identifying a norm capturing the effect of the forcing governed by the Poisson equation, we give a detailed spectrum analysis on the linearized Vlasov-Poisson-Boltzmann system around a global Maxwellian. It is shown that the electric field governed by the self-consistent Poisson equation plays a key role in the analysis so that the spectrum structure is genuinely different from the well-known one of the Boltzmann equation. Based on this, we give the optimal time decay rates of solutions to the equilibrium.Free boundary problem in a polymer solution modelhttps://zbmath.org/1472.354232021-11-25T18:46:10.358925Z"Petrova, A. G."https://zbmath.org/authors/?q=ai:petrova.anna-georgevna"Pukhnachev, V. V."https://zbmath.org/authors/?q=ai:pukhnachov.vladislav-vThe authors consider the integro-differential equation
\[
\frac{\partial w}{\partial t}+\frac{\partial w}{\partial y}\int_{0}^{y}w(z,t)dz-w^{2}=\frac{\partial^{2}w}{\partial y^{2}}+\gamma (\frac{\partial^{3}w}{\partial y^{2}\partial t}+\frac{\partial^{3}w}{\partial y^{3}}\int_{0}^{y}w(z,t)dz- \frac{\partial^{2}w}{\partial y^{2}}),
\]
posed in the domain \(\Omega_{T} = \{y,t:0 < y < h(t)\), \(0\leq t\leq T\}\). This model accounts for the flow of a mixture of water and polymer. This equation is completed with: \(\frac{dh}{dt}=\int_{0}^{h}w(y,t)dy\). The boundary conditions \(w(0,t)=0\) and \(\frac{\partial w}{\partial y}+\gamma (\frac{\partial^{2}w}{\partial y\partial t}+ \frac{\partial^{2}w}{\partial y^{2}}\int_{0}^{h}w(y,t)dy-w\frac{\partial w}{\partial y})(h(t),t)=0\) are added, together with the initial conditions \( w(y,0)=w_{0}(y)\), \(0\leq y\leq 1\), \(h(0)=1\). Here \(\gamma >0\) is a constant and \(w_{0}\) is a smooth (\(C^{3}\)) function of \(y\) satisfying the conditions \( w_{0}(0)=w_{0}^{\prime}(1)=0\). The first main result proves the existence of a local in time strong solution (\(h\in C^{1}([0,t^{\ast}])\), \(w\in C^{3,1}([0,h(t)]\times \lbrack 0,t^{\ast}])\)) to this problem. If the initial condition further satisfies \(w_{0}(y)\leq 0\), \(w_{0}(y)-\gamma w_{0}^{\prime \prime}(y)\leq 0\), the authors prove the existence of a classical solution \(h\in C^{1}([0,T])\), \(w\in C^{3,1}([0,h(t)]\times \lbrack 0,T])\) to the above problem. Both existence results are obtained through appropriate transformations and using Schauder's theorem. The authors then consider the case where \(\gamma\) tends to 0 and they observe that the problem turns into that of the deformation of a strip of viscous fluid. They here prove that the solution to this problem is destructed in finite time. They finally introduce asymptotic expansions with respect to \(\gamma\) and they express the second term of this asymptotic expansion.Asymptotic formulas for determinants of a special class of Toeplitz + Hankel matriceshttps://zbmath.org/1472.470212021-11-25T18:46:10.358925Z"Basor, Estelle"https://zbmath.org/authors/?q=ai:basor.estelle-l"Ehrhardt, Torsten"https://zbmath.org/authors/?q=ai:ehrhardt.torstenSummary: We compute the asymptotics of the determinants of certain \(n \times n\) Toeplitz + Hankel matrices \( T_{n}(a)+H_n(b)\) as \( n\rightarrow \infty \) with symbols of Fisher-Hartwig type. More specifically, we consider the case where \(a\) has zeros and poles and where \(b\) is related to \(a\) in specific ways. Previous results of \textit{P. Deift} et al. [Ann. Math. (2) 174, No. 2, 1243--1299 (2011; Zbl 1232.15006)] dealt with the case where \(a\) is even. We are generalizing this in a mild way to certain non-even symbols.
For the entire collection see [Zbl 1367.47005].Natural boundary for a sum involving Toeplitz determinantshttps://zbmath.org/1472.470232021-11-25T18:46:10.358925Z"Tracy, Craig A."https://zbmath.org/authors/?q=ai:tracy.craig-a"Widom, Harold"https://zbmath.org/authors/?q=ai:widom.haroldSummary: In the theory of the two-dimensional Ising model, the \textit{diagonal susceptibility} is equal to a sum involving Toeplitz determinants. In terms of a parameter \(k\), the diagonal susceptibility is analytic for \(| k | < 1\), and the authors proved in [J. Math. Phys. 54, No. 12, 123302, 9 p. (2013; Zbl 1288.82018)] the conjecture that this function has the unit circle as a natural boundary. The symbol of the Toeplitz determinants is a \(k\)-deformation of one with a single singularity on the unit circle. Here we extend the result, first, to deformations of a larger class of symbols with a single singularity on the unit circle, and then to deformations of (almost) general Fisher-Hartwig symbols.
For the entire collection see [Zbl 1367.47005].Wegner estimate for random divergence-type operators monotone in the randomnesshttps://zbmath.org/1472.470362021-11-25T18:46:10.358925Z"Dicke, Alexander"https://zbmath.org/authors/?q=ai:dicke.alexanderSummary: In this note, a Wegner estimate for random divergence-type operators that are monotone in the randomness is proven. The proof is based on a recently shown unique continuation estimate for the gradient and the ensuing eigenvalue liftings. The random model which is studied here contains quite general random perturbations, among others, some that have a non-linear dependence on the random parameters.Sharp phase transition for the continuum Widom-Rowlinson modelhttps://zbmath.org/1472.600192021-11-25T18:46:10.358925Z"Dereudre, David"https://zbmath.org/authors/?q=ai:dereudre.david"Houdebert, Pierre"https://zbmath.org/authors/?q=ai:houdebert.pierreSummary: The Widom-Rowlinson model (or the Area-interaction model) is a Gibbs point process in \(\mathbb{R}^d\) with the formal Hamiltonian defined as the volume of \(\cup_{x\in\omega}B_1(x)\), where \(\omega\) is a locally finite configuration of points and \(B_1(x)\) denotes the unit closed ball centred at \(x\). The model is also tuned by two other parameters: the activity \(z>0\) related to the intensity of the process and the inverse temperature \(\beta\geq 0\) related to the strength of the interaction. In the present paper we investigate the phase transition of the model in the point of view of percolation theory and the liquid-gas transition. First, considering the graph connecting points with distance smaller than \(2r>0\), we show that for any \(\beta\geq 0\), there exists \(0<\widetilde{z}_c^a(\beta ,r)<+\infty\) such that an exponential decay of connectivity at distance \(n\) occurs in the subcritical phase (i.e. \(z<\widetilde{z}_c^a(\beta ,r))\) and a linear lower bound of the connection at infinity holds in the supercritical case (i.e. \(z>\widetilde{z}_c^a(\beta,r))\). These results are in the spirit of recent works using the theory of randomised tree algorithms [\textit{H. Duminil-Copin} et al., Probab. Theory Relat. Fields 173, No. 1--2, 479--490 (2019; Zbl 07030876); Ann. Math. (2) 189, No. 1, 75--99 (2019; Zbl 07003145)]. Secondly we study a standard liquid-gas phase transition related to the uniqueness/non-uniqueness of Gibbs states depending on the parameters \(z,\beta\). Old results [\textit{D. Ruelle}, ``Existence of a phase transition in a continuous classical system'', Phys. Rev. Lett. 27, 1040--1041 (1971; \url{doi:10.1103/PhysRevLett.27.1040}; \textit{A. Mazel} et al., J. Stat. Phys. 159, No. 5, 1040--1086 (2015; Zbl 1329.82013)] claim that a non-uniqueness regime occurs for \(z=\beta\) large enough and it is conjectured that the uniqueness should hold outside such an half line \((z=\beta\geq\beta_c>0)\). We solve partially this conjecture in any dimension by showing that for \(\beta\) large enough the non-uniqueness holds if and only if \(z=\beta\). We show also that this critical value \(z=\beta\) corresponds to the percolation threshold \(\widetilde{z}_c^a(\beta,r)=\beta\) for \(\beta\) large enough, providing a straight connection between these two notions of phase transition.Scaling limits and fluctuations for random growth under capacity rescalinghttps://zbmath.org/1472.600452021-11-25T18:46:10.358925Z"Liddle, George"https://zbmath.org/authors/?q=ai:liddle.george"Turner, Amanda"https://zbmath.org/authors/?q=ai:turner.amanda-gSummary: We evaluate a strongly regularised version of the Hastings-Levitov model \(\mathrm{HL}(\alpha)\) for \(0\leq\alpha<2\). Previous results have concentrated on the small-particle limit where the size of the attaching particle approaches zero in the limit. However, we consider the case where we rescale the whole cluster by its capacity before taking limits, whilst keeping the particle size fixed. We first consider the case where \(\alpha=0\) and show that under capacity rescaling, the limiting structure of the cluster is not a disk, unlike in the small-particle limit. Then we consider the case where \(0<\alpha<2\) and show that under the same rescaling the cluster approaches a disk. We also evaluate the fluctuations and show that, when represented as a holomorphic function, they behave like a Gaussian field dependent on \(\alpha\). Furthermore, this field becomes degenerate as \(\alpha\) approaches 0 and 2, suggesting the existence of phase transitions at these values.Quantum fluctuations and large-deviation principle for microscopic currents of free fermions in disordered mediahttps://zbmath.org/1472.600502021-11-25T18:46:10.358925Z"Bru, Jean-Bernard"https://zbmath.org/authors/?q=ai:bru.jean-bernard"de Siqueira Pedra, Walter"https://zbmath.org/authors/?q=ai:de-siqueira-pedra.walter"Ratsimanetrimanana, Antsa"https://zbmath.org/authors/?q=ai:ratsimanetrimanana.antsaSummary: We extend the large-deviation results obtained by \textit{N. J. B. Aza} and the present authors [J. Math. Pures Appl. (9) 125, 209--246 (2019; Zbl 1419.82058)] on atomic-scale conductivity theory of free lattice fermions in disordered media. Disorder is modeled by a random external potential, as in the celebrated Anderson model, and a nearest-neighbor hopping term with random complex-valued amplitudes. In accordance with experimental observations, via the large-deviation formalism, our previous paper showed in this case that quantum uncertainty of microscopic electric current densities around their (classical) macroscopic value is suppressed, exponentially fast with respect to the volume of the region of the lattice where an external electric field is applied. Here, the quantum fluctuations of linear response currents are shown to exist in the thermodynamic limit, and we mathematically prove that they are related to the rate function of the large-deviation principle associated with current densities. We also demonstrate that, in general, they do not vanish (in the thermodynamic limit), and the quantum uncertainty around the macroscopic current density disappears exponentially fast with an exponential rate proportional to the squared deviation of the current from its macroscopic value and the inverse current fluctuation, with respect to growing space (volume) scales.Imaginary multiplicative chaos: moments, regularity and connections to the Ising modelhttps://zbmath.org/1472.600642021-11-25T18:46:10.358925Z"Junnila, Janne"https://zbmath.org/authors/?q=ai:junnila.janne"Saksman, Eero"https://zbmath.org/authors/?q=ai:saksman.eero"Webb, Christian"https://zbmath.org/authors/?q=ai:webb.christianSummary: In this article we study imaginary Gaussian multiplicative chaos -- namely a family of random generalized functions which can formally be written as \(e^{iX(x)}\), where \(X\) is a log-correlated real-valued Gaussian field on \(\mathbb{R}^d\), that is, it has a logarithmic singularity on the diagonal of its covariance. We study basic analytic properties of these random generalized functions, such as what spaces of distributions these objects live in, along with their basic stochastic properties, such as moment and tail estimates.
After this, we discuss connections between imaginary multiplicative chaos and the critical planar Ising model, namely that the scaling limit of the spin field of the critical planar XOR-Ising model can be expressed in terms of the cosine of the Gaussian free field, that is, the real part of an imaginary multiplicative chaos distribution. Moreover, if one adds a magnetic perturbation to the XOR-Ising model, then the scaling limit of the spin field can be expressed in terms of the cosine of the sine-Gordon field, which can also be viewed as the real part of an imaginary multiplicative chaos distribution.
The first sections of the article have been written in the style of a review, and we hope that the text will also serve as an introduction to imaginary chaos for an uninitiated reader.Mixing time and eigenvalues of the abelian sandpile Markov chainhttps://zbmath.org/1472.601192021-11-25T18:46:10.358925Z"Jerison, Daniel C."https://zbmath.org/authors/?q=ai:jerison.daniel-c"Levine, Lionel"https://zbmath.org/authors/?q=ai:levine.lionel"Pike, John"https://zbmath.org/authors/?q=ai:pike.johnSummary: The abelian sandpile model defines a Markov chain whose states are integer-valued functions on the vertices of a simple connected graph \(G\). By viewing this chain as a (nonreversible) random walk on an abelian group, we give a formula for its eigenvalues and eigenvectors in terms of ``multiplicative harmonic functions'' on the vertices of \(G\). We show that the spectral gap of the sandpile chain is within a constant factor of the length of the shortest noninteger vector in the dual Laplacian lattice, while the mixing time is at most a constant times the smoothing parameter of the Laplacian lattice. We find a surprising inverse relationship between the spectral gap of the sandpile chain and that of simple random walk on \(G\): If the latter has a sufficiently large spectral gap, then the former has a small gap! In the case where \(G\) is the complete graph on \(n\) vertices, we show that the sandpile chain exhibits cutoff at time \(\frac{1}{4\pi ^2}n^3\log n\).Mixing of the square plaquette model on a critical length scalehttps://zbmath.org/1472.601262021-11-25T18:46:10.358925Z"Chleboun, Paul"https://zbmath.org/authors/?q=ai:chleboun.paul"Smith, Aaron"https://zbmath.org/authors/?q=ai:smith.aaron-carl|smith.aaron-mAuthors' abstract: Plaquette models are short range ferromagnetic spin models that play a key role in the dynamic facilitation approach to the liquid glass transition. In this paper we study the dynamics of the square plaquette model at the smallest of the three critical length scales discovered in [the first author et al., J. Stat. Phys. 169, No. 3, 441--471 (2017; Zbl 1382.82009)]. Our main results are estimates of the spectral gap and mixing time for two natural boundary conditions. As a consequence, we observe that these time scales depend heavily on the boundary condition in this scaling regime.Mixing time and cutoff for the weakly asymmetric simple exclusion processhttps://zbmath.org/1472.601272021-11-25T18:46:10.358925Z"Labbé, Cyril"https://zbmath.org/authors/?q=ai:labbe.cyril"Lacoin, Hubert"https://zbmath.org/authors/?q=ai:lacoin.hubertSummary: We consider the simple exclusion process with \(k\) particles on a segment of length \(N\) performing random walks with transition \(p > 1/2\) to the right and \(q = 1 - p\) to the left. We focus on the case where the asymmetry in the jump rates \(b = p - q > 0\) vanishes in the limit when \(N\) and \(k\) tend to infinity, and obtain sharp asymptotics for the mixing times of this sequence of Markov chains in the two cases where the asymmetry is either much larger or much smaller than \((\log k)/N\). We show that in the former case \((b \gg (\log k)/N)\), the mixing time corresponds to the time needed to reach macroscopic equilibrium, like for the strongly asymmetric (i.e., constant \(b)\) case studied in [the authors, Ann. Probab. 47, No. 3, 1541--1586 (2019; Zbl 1466.60152)], while the latter case \((b\ll (\log k)/N)\) macroscopic equilibrium is not sufficient for mixing and one must wait till local fluctuations equilibrate, similarly to what happens in the symmetric case worked out in
[the second author, Ann. Probab. 44, No. 2, 1426--1487 (2016; Zbl 1408.60061)]. In both cases, convergence to equilibrium is abrupt: we have a cutoff phenomenon for the total-variation distance. We present a conjecture for the remaining regime when the asymmetry is of order \((\log k)/N\).Second time scale of the metastability of reversible inclusion processeshttps://zbmath.org/1472.601312021-11-25T18:46:10.358925Z"Kim, Seonwoo"https://zbmath.org/authors/?q=ai:kim.seonwooSummary: We investigate the \textit{second time scale} of the metastable behavior of the reversible inclusion process in an extension of the study by \textit{A. Bianchi} et al. [Electron. J. Probab. 22, Paper No. 70, 34 p. (2017; Zbl 1386.60319)], which presented the first time scale of the same model and conjectured the scheme of multiple time scales. We show that \(N/d_N^2\) is indeed the correct second time scale for the most general class of reversible inclusion processes, and thus prove the first conjecture of the foresaid study. Here, \(N\) denotes the number of particles, and \(d_N\) denotes the small scale of randomness of the system. The main obstacles of this research arise in \textit{calculating the sharp asymptotics for the capacities}, and in the fact that the methods employed in the former study are not directly applicable due to the complex geometry of particle configurations. To overcome these problems, we first \textit{thoroughly examine the landscape of the transition rates} to obtain a proper test function of the equilibrium potential, which provides the upper bound for the capacities. Then, we \textit{modify the induced test flow} and \textit{precisely estimate the equilibrium potential near the metastable valleys} to obtain the correct lower bound for the capacities.Diffusions interacting through a random matrix: universality via stochastic Taylor expansionhttps://zbmath.org/1472.601372021-11-25T18:46:10.358925Z"Dembo, Amir"https://zbmath.org/authors/?q=ai:dembo.amir"Gheissari, Reza"https://zbmath.org/authors/?q=ai:gheissari.rezaSummary: Consider \((X_i(t))\) solving a system of \(N\) stochastic differential equations interacting through a random matrix \({\mathbf{J}} = (J_{ij})\) with independent (not necessarily identically distributed) random coefficients. We show that the trajectories of averaged observables of \((X_i(t))\), initialized from some \(\mu\) independent of \({\mathbf{J}} \), are universal, i.e., only depend on the choice of the distribution \(\mathbf{J}\) through its first and second moments (assuming e.g., sub-exponential tails). We take a general combinatorial approach to proving universality for dynamical systems with random coefficients, combining a stochastic Taylor expansion with a moment matching-type argument. Concrete settings for which our results imply universality include aging in the spherical SK spin glass, and Langevin dynamics and gradient flows for symmetric and asymmetric Hopfield networks.Spectral gap in mean-field \({\mathcal{O}}(n)\)-modelhttps://zbmath.org/1472.601502021-11-25T18:46:10.358925Z"Becker, Simon"https://zbmath.org/authors/?q=ai:becker.simon"Menegaki, Angeliki"https://zbmath.org/authors/?q=ai:menegaki.angelikiSummary: We study the dependence of the spectral gap for the generator of the Ginzburg-Landau dynamics for all \(\mathcal O(n)\)-\textit{models} with mean-field interaction and magnetic field, below and at the critical temperature on the number \(N\) of particles. For our analysis of the Gibbs measure, we use a one-step renormalization approach and semiclassical methods to study the eigenvalue-spacing of an auxiliary Schrödinger operator.Spread of an infection on the zero range processhttps://zbmath.org/1472.601542021-11-25T18:46:10.358925Z"Baldasso, Rangel"https://zbmath.org/authors/?q=ai:baldasso.rangel"Teixeira, Augusto"https://zbmath.org/authors/?q=ai:teixeira.augusto-quadrosSummary: We study the spread of an infection on top of a moving population. The environment evolves as a zero range process on the integer lattice starting in equilibrium. At time zero, the set of infected particles is composed by those which are on the negative axis, while particles at the right of the origin are considered healthy. A healthy particle immediately becomes infected if it shares a site with an infected particle. We prove that the front of the infection wave travels to the right with positive and finite velocity. As a central step in the proof of these results, we prove a space-time decoupling for the zero range process which is interesting on its own. Using a sprinkling technique, we derive an estimate on the correlation of functions of the space of trajectories whose supports are sufficiently far away.Asymptotic behavior of the integrated density of states for random point fields associated with certain Fredholm determinantshttps://zbmath.org/1472.601562021-11-25T18:46:10.358925Z"Ueki, Naomasa"https://zbmath.org/authors/?q=ai:ueki.naomasaSummary: The asymptotic behavior of the integrated density of states of a Schrödinger operator with positive potentials located around all sample points of some random point field at the infimum of the spectrum is investigated. The random point field is taken from a subclass of the class given by \textit{T. Shirai} and \textit{Y. Takahashi} [J. Funct. Anal. 205, No. 2, 414--463 (2003; Zbl 1051.60052)] in terms of the Fredholm determinant. In the subclass, the obtained leading orders are the same as the well known results for the Poisson point fields, and the character of the random field appears in the leading constants. The random point fields associated with the sine kernel and the Ginibre random point field are well studied examples not included in the above subclass, though they are included in the class by Shirai and Takahashi. By applying the results on asymptotics of the hole probability for these random fields, the corresponding asymptotic behaviors of the densities of states are also investigated in the case where the single site potentials have compact supports. The same method also applies to another well studied example, the zeros of a Gaussian random analytic function.Model reduction for kinetic equations: moment approximations and hierarchical approximate proper orthogonal decompositionhttps://zbmath.org/1472.650042021-11-25T18:46:10.358925Z"Leibner, Tobias"https://zbmath.org/authors/?q=ai:leibner.tobias(no abstract)Hyperbolic models for the spread of epidemics on networks: kinetic description and numerical methodshttps://zbmath.org/1472.651052021-11-25T18:46:10.358925Z"Bertaglia, Giulia"https://zbmath.org/authors/?q=ai:bertaglia.giulia"Pareschi, Lorenzo"https://zbmath.org/authors/?q=ai:pareschi.lorenzoIn this work, a novel SIR-type kinetic transport model for the spread of infectious diseases on networks is developed, where S is the number of susceptible individuals, I is the number of infected individuals, and R is the number of recovered individuals. The hyperbolic system describes at a macroscopic level the propagation of epidemics at finite speeds, recovering the classical one-dimensional reaction-diffusion model as relaxation times and characteristic speeds of each compartment of the population (susceptible, infectious and recovered individuals) tend to zero and infinity, respectively. As discretization for this interesting model, the authors suggest a finite-volume IMEX method able to maintain the consistency with the diffusive limit without restrictions due to the scaling parameters. Several numerical tests for simple epidemic network structures are presented to confirm the ability of the model to correctly describe the spread of an epidemic.Affine invariant interacting Langevin dynamics for Bayesian inferencehttps://zbmath.org/1472.651182021-11-25T18:46:10.358925Z"Garbuno-Inigo, Alfredo"https://zbmath.org/authors/?q=ai:garbuno-inigo.alfredo"Nüsken, Nikolas"https://zbmath.org/authors/?q=ai:nusken.nikolas"Reich, Sebastian"https://zbmath.org/authors/?q=ai:reich.sebastianThis paper proposes a computational method for generating samples from a given high-dimensional target distribution of the form \[ \pi(u) = \frac1Z \exp(-\Phi(u)) \] where \(\Phi\) is a suitable potential and \(Z\) is a normalization constant; this is a fundamental task in, e.g., Bayesian inverse problems. As an alternative to the widely known (Markov chain) Monte Carlo methods, the proposed method is based on Langevin dynamics under which the target distribution is invariant. Specifically, they propose a stochastic process of \(N\) interacting particles given by \[ d u^{(i)}_t = -C(U_t) \nabla_{u^{(i)}}\Phi(u^{(i)}_t)dt + \frac{D+1}{N}(u^{(i)}_t - m(U_t))dt + \sqrt2 C^{1/2}(U_t)dW_t^{(i)}, \] where \(u^{(i)}_t\in\mathbb{R}^D\) denotes position of the \(i\)th particle at time \(t\) (which are all collected into the vector \(U_t\)), \(C(U_t)\) is the empirical covariance matrix, \(m(U_t)\) is the empirical mean, and \(C^{1/2}(U_t)\) is a generalized square root than can be directly computed using the deviations of the particles from the empirical mean. The second term here is a correction term that guarantees for \(N>D+1\) (under suitable assumptions on the potential and the initial ensemble) that these dynamics are invariant under affine transformations, which prevents inefficient sampling if the empirical covariance matrix is a poor approximation of the target covariance measure in Bayesian inverse problems with Gaussian posteriors.
They also provide a gradient-free variant that replaces \(\nabla_{u^{(i)}}\Phi(u^{(i)}_t)\) by an approximation that is exact for Bayesian inverse problems with affine forward operators and is related to classical Ensemble Kalman-Bucy Filter as well as to the more recent Ensemble Kalman inversion.
The performance of this method is illustrated for the typical model problem of Darcy flow inversion.High-order BDF fully discrete scheme for backward fractional Feynman-Kac equation with nonsmooth datahttps://zbmath.org/1472.651262021-11-25T18:46:10.358925Z"Sun, Jing"https://zbmath.org/authors/?q=ai:sun.jing"Nie, Daxin"https://zbmath.org/authors/?q=ai:nie.daxin"Deng, Weihua"https://zbmath.org/authors/?q=ai:deng.weihuaSummary: The Feynman-Kac equation governs the distribution of the statistical observable -- functional, having wide applications in almost all disciplines. After overcoming some challenges from the time-space coupled nonlocal operator and the possible low regularity of functional, this paper develops the high-order fully discrete scheme for the backward fractional Feynman-Kac equation by using backward difference formulas (BDF) convolution quadrature in time, finite element method in space, and some correction terms. With a systematic correction, the high convergence order is achieved up to 6 in time, without deteriorating the optimal convergence in space and without the regularity requirement on the solution. Finally, the extensive numerical experiments validate the effectiveness of the high-order schemes.Wave polarization and dynamic degeneracy in a chiral elastic latticehttps://zbmath.org/1472.700392021-11-25T18:46:10.358925Z"Carta, G."https://zbmath.org/authors/?q=ai:carta.giorgio"Jones, I. S."https://zbmath.org/authors/?q=ai:jones.ian-s"Movchan, N. V."https://zbmath.org/authors/?q=ai:movchan.natasha-v|movchan.natalia-v"Movchan, A. B."https://zbmath.org/authors/?q=ai:movchan.alexander-bSummary: This paper addresses fundamental questions arising in the theory of Bloch-Floquet waves in chiral elastic lattice systems. This area has received a significant attention in the context of `topologically protected' waveforms. Although practical applications of chiral elastic lattices are widely appreciated, especially in problems of controlling low-frequency vibrations, wave polarization and filtering, the fundamental questions of the relationship of these lattices to classical waveforms associated with longitudinal and shear waves retain a substantial scope for further development. The notion of chirality is introduced into the systematic analysis of dispersive elastic waves in a doubly-periodic lattice. Important quantitative characteristics of the dynamic response of the lattice, such as lattice flux and lattice circulation, are used in the analysis along with the novel concept of `vortex waveforms' that characterize the dynamic response of the chiral system. We note that the continuum concepts of pressure and shear waves do not apply for waves in a lattice, especially in the case when the wavelength is comparable with the size of the elementary cell of the periodic structure. Special critical regimes are highlighted when vortex waveforms become dominant. Analytical findings are accompanied by illustrative numerical simulations.Plasmonic modes in cylindrical nanoparticles and dimershttps://zbmath.org/1472.741182021-11-25T18:46:10.358925Z"Downing, Charles A."https://zbmath.org/authors/?q=ai:downing.charles-a"Weick, Guillaume"https://zbmath.org/authors/?q=ai:weick.guillaumeSummary: We present analytical expressions for the resonance frequencies of the plasmonic modes hosted in a cylindrical nanoparticle within the quasi-static approximation. Our theoretical model gives us access to both the longitudinally and transversally polarized dipolar modes for a metallic cylinder with an arbitrary aspect ratio, which allows us to capture the physics of both plasmonic nanodisks and nanowires. We also calculate quantum mechanical corrections to these resonance frequencies due to the spill-out effect, which is of relevance for cylinders with nanometric dimensions. We go on to consider the coupling of localized surface plasmons in a dimer of cylindrical nanoparticles, which leads to collective plasmonic excitations. We extend our theoretical formalism to construct an analytical model of the dimer, describing the evolution with the inter-nanoparticle separation of the resultant bright and dark collective modes. We comment on the renormalization of the coupled mode frequencies due to the spill-out effect, and discuss some methods of experimental detection.A pseudo-anelastic model for stress softening in liquid crystal elastomershttps://zbmath.org/1472.760042021-11-25T18:46:10.358925Z"Mihai, L. Angela"https://zbmath.org/authors/?q=ai:mihai.l-angela"Goriely, Alain"https://zbmath.org/authors/?q=ai:goriely.alainSummary: Liquid crystal elastomers exhibit stress softening with residual strain under cyclic loads. Here, we model this phenomenon by generalizing the classical pseudo-elastic formulation of the Mullins effect in rubber. Specifically, we modify the neoclassical strain-energy density of liquid crystal elastomers, depending on the deformation and the nematic director, by incorporating two continuous variables that account for stress softening and the associated set strain. As the material behaviour is governed by different forms of the strain-energy density on loading and unloading, the model is referred to as pseudo-anelastic. We then analyse qualitatively the mechanical responses of the material under cyclic uniaxial tension, which is easier to reproduce in practice, and further specialize the model in order to calibrate its parameters to recent experimental data at different temperatures. The excellent agreement between the numerical and experimental results confirms the suitability of our approach. Since the pseudo-energy function is controlled by the strain-energy density for the primary deformation, it is valid also for materials under multiaxial loads. Our study is relevant to mechanical damping applications and serves as a motivation for further experimental tests.Fluctuation theorem and extended thermodynamics of turbulencehttps://zbmath.org/1472.760462021-11-25T18:46:10.358925Z"Porporato, Amilcare"https://zbmath.org/authors/?q=ai:porporato.amilcare"Hooshyar, Milad"https://zbmath.org/authors/?q=ai:hooshyar.milad"Bragg, Andrew D."https://zbmath.org/authors/?q=ai:bragg.andrew-d"Katul, Gabriel"https://zbmath.org/authors/?q=ai:katul.gabriel-gSummary: Turbulent flows are out-of-equilibrium because the energy supply at large scales and its dissipation by viscosity at small scales create a net transfer of energy among all scales. This energy cascade is modelled by approximating the spectral energy balance with a nonlinear Fokker-Planck equation consistent with accepted phenomenological theories of turbulence. The steady-state contributions of the drift and diffusion in the corresponding Langevin equation, combined with the killing term associated with the dissipation, induce a stochastic energy transfer across wavenumbers. The fluctuation theorem is shown to describe the scale-wise statistics of forward and backward energy transfer and their connection to irreversibility and entropy production. The ensuing turbulence entropy is used to formulate an extended turbulence thermodynamics.A fully coupled hybrid lattice Boltzmann and finite difference method-based study of transient electrokinetic flowshttps://zbmath.org/1472.760672021-11-25T18:46:10.358925Z"Basu, Himadri Sekhar"https://zbmath.org/authors/?q=ai:basu.himadri-sekhar"Bahga, Supreet Singh"https://zbmath.org/authors/?q=ai:singh-bahga.supreet"Kondaraju, Sasidhar"https://zbmath.org/authors/?q=ai:kondaraju.sasidharSummary: Transient electrokinetic (EK) flows involve the transport of conductivity gradients developed as a result of mixing of ionic species in the fluid, which in turn is affected by the electric field applied across the channel. The presence of three different coupled equations with corresponding different time scales makes it difficult to model the problem using the lattice Boltzmann method (LBM). The present work aims to develop a hybrid LBM and finite difference method (FDM)-based model which can be used to study the electro-osmotic flows (EOFs) and the onset of EK instabilities using an Ohmic model, where fluid and conductivity transport are solved using LBM and the electric field is solved using FDM. The model developed will be used to simulate three different problems: (i) EOF with varying zeta-potential on the wall, (ii) similitude in EOF, and (iii) EK instabilities due to the presence of conductivity gradients. Problems (i) and (ii) will be compared with the analytical results and problem (iii) will be compared with the simulations of a spectral method-based numerical model. The results obtained from the present simulations will show that the developed model is capable of studying transient EK flows and of predicting the onset of instability.Collective vibrations of a hydrodynamic active latticehttps://zbmath.org/1472.760692021-11-25T18:46:10.358925Z"Thomson, S. J."https://zbmath.org/authors/?q=ai:thomson.s-j"Durey, M."https://zbmath.org/authors/?q=ai:durey.matthew"Rosales, R. R."https://zbmath.org/authors/?q=ai:rosales.rodolfo-rubenSummary: Recent experiments show that quasi-one-dimensional lattices of self-propelled droplets exhibit collective instabilities in the form of out-of-phase oscillations and solitary-like waves. This hydrodynamic lattice is driven by the external forcing of a vertically vibrating fluid bath, which invokes a field of subcritical Faraday waves on the bath surface, mediating the spatio-temporal droplet coupling. By modelling the droplet lattice as a memory-endowed system with spatially non-local coupling, we herein rationalize the form and onset of instability in this new class of dynamical oscillator. We identify the memory-driven instability of the lattice as a function of the number of droplets, and determine equispaced lattice configurations precluded by geometrical constraints. Each memory-driven instability is then classified as either a super- or subcritical Hopf bifurcation via a systematic weakly nonlinear analysis, rationalizing experimental observations. We further discover a previously unreported symmetry-breaking instability, manifest as an oscillatory-rotary motion of the lattice. Numerical simulations support our findings and prompt further investigations of this nonlinear dynamical system.A BGK model for high temperature rarefied gas flowshttps://zbmath.org/1472.760782021-11-25T18:46:10.358925Z"Baranger, C."https://zbmath.org/authors/?q=ai:baranger.celine"Dauvois, Y."https://zbmath.org/authors/?q=ai:dauvois.y"Marois, G."https://zbmath.org/authors/?q=ai:marois.g"Mathé, J."https://zbmath.org/authors/?q=ai:mathe.jordane|mathe.j-m|mathe.johan"Mathiaud, J."https://zbmath.org/authors/?q=ai:mathiaud.julien"Mieussens, L."https://zbmath.org/authors/?q=ai:mieussens.lucSummary: High temperature gases, for instance in hypersonic reentry flows, show complex phenomena like excitation of rotational and vibrational energy modes, and even chemical reactions. For flows in the continuous regime, simulation codes use analytic or tabulated constitutive laws for pressure and temperature. In this paper, we propose a BGK model which is consistent with any arbitrary constitutive laws, and which is designed to make high temperature gas flow simulations in the rarefied regime. A Chapman-Enskog analysis gives the corresponding transport coefficients. Our approach is illustrated by a numerical comparison with a compressible Navier-Stokes solver with rotational and vibrational non equilibrium. The BGK approach gives a deterministic solver with a computational cost which is close to that of a simple monoatomic gas.Improved phase-field models of melting and dissolution in multi-component flowshttps://zbmath.org/1472.761052021-11-25T18:46:10.358925Z"Hester, Eric W."https://zbmath.org/authors/?q=ai:hester.eric-w"Couston, Louis-Alexandre"https://zbmath.org/authors/?q=ai:couston.louis-alexandre"Favier, Benjamin"https://zbmath.org/authors/?q=ai:favier.benjamin"Burns, Keaton J."https://zbmath.org/authors/?q=ai:burns.keaton-j"Vasil, Geoffrey M."https://zbmath.org/authors/?q=ai:vasil.geoffrey-mSummary: We develop and analyse the first second-order phase-field model to combine melting and dissolution in multi-component flows. This provides a simple and accurate way to simulate challenging phase-change problems in existing codes. Phase-field models simplify computation by describing separate regions using a smoothed phase field. The phase field eliminates the need for complicated discretizations that track the moving phase boundary. However, standard phase-field models are only first-order accurate. They often incur an error proportional to the thickness of the diffuse interface. We eliminate this dominant error by developing a general framework for asymptotic analysis of diffuse-interface methods in arbitrary geometries. With this framework, we can consistently unify previous second-order phase-field models of melting and dissolution and the volume-penalty method for fluid-solid interaction. We finally validate second-order convergence of our model in two comprehensive benchmark problems using the open-source spectral code Dedalus.Magnetic reconnection in partially ionized plasmashttps://zbmath.org/1472.780032021-11-25T18:46:10.358925Z"Ni, Lei"https://zbmath.org/authors/?q=ai:ni.lei"Ji, Hantao"https://zbmath.org/authors/?q=ai:ji.hantao"Murphy, Nicholas A."https://zbmath.org/authors/?q=ai:murphy.nicholas-a"Jara-Almonte, Jonathan"https://zbmath.org/authors/?q=ai:jara-almonte.jonathanSummary: Magnetic reconnection has been intensively studied in fully ionized plasmas. However, plasmas are often partially ionized in astrophysical environments. The interactions between the neutral particles and ionized plasmas might strongly affect the reconnection mechanisms. We review magnetic reconnection in partially ionized plasmas in different environments from theoretical, numerical, observational and experimental points of view. We focus on mechanisms which make magnetic reconnection fast enough to compare with observations, especially on the reconnection events in the low solar atmosphere. The heating mechanisms and the related observational evidence of the reconnection process in the partially ionized low solar atmosphere are also discussed. We describe magnetic reconnection in weakly ionized astrophysical environments, including the interstellar medium and protostellar discs. We present recent achievements about fast reconnection in laboratory experiments for partially ionized plasmas.Loss-less propagation, elastic and inelastic interaction of electromagnetic soliton in an anisotropic ferromagnetic nanowirehttps://zbmath.org/1472.780112021-11-25T18:46:10.358925Z"Senthil Kumar, V."https://zbmath.org/authors/?q=ai:kumar.v-senthil"Kavitha, L."https://zbmath.org/authors/?q=ai:kavitha.louis"Boopathy, C."https://zbmath.org/authors/?q=ai:boopathy.c"Gopi, D."https://zbmath.org/authors/?q=ai:gopi.dSummary: Nonlinear interaction of electromagnetic solitons leads to a plethora of interesting physical phenomena in the diverse area of science that include magneto-optics based data storage industry. We investigate the nonlinear magnetization dynamics of a one-dimensional anisotropic ferromagnetic nanowire. The famous Landau-Lifshitz-Gilbert equation (LLG) describes the magnetization dynamics of the ferromagnetic nanowire and the Maxwell's equations govern the propagation dynamics of electromagnetic wave passing through the axis of the nanowire. We perform a uniform expansion of magnetization and magnetic field along the direction of propagation of electromagnetic wave in the framework of reductive perturbation method. The excitation of magnetization of the nanowire is restricted to the normal plane at the lowest order of perturbation and goes out of plane for higher orders. The dynamics of the ferromagnetic nanowire is governed by the modified Korteweg-de Vries (mKdV) equation and the perturbed modified Korteweg-de Vries (pmKdV) equation for the lower and higher values of damping respectively. We invoke the Hirota bilinearization procedure to mKdV and pmKdV equation to construct the multi-soliton solutions, and explicitly analyze the nature of collision phenomena of the co-propagating EM solitons for the above mentioned lower and higher values of Gilbert-damping due to the precessional motion of the ferromagnetic spin. The EM solitons appearing in the higher damping regime exhibit elastic collision thus yielding the fascinating state restoration property, whereas those of lower damping regime exhibit inelastic collision yielding the solitons of suppressed intensity profiles. The propagation of EM soliton in the nanoscale magnetic wire has potential technological applications in optimizing the magnetic storage devices and magneto-electronics.Analytical model for electrohydrodynamic thrusthttps://zbmath.org/1472.780122021-11-25T18:46:10.358925Z"Vaddi, Ravi Sankar"https://zbmath.org/authors/?q=ai:vaddi.ravi-sankar"Guan, Yifei"https://zbmath.org/authors/?q=ai:guan.yifei"Mamishev, Alexander"https://zbmath.org/authors/?q=ai:mamishev.alexander-v"Novosselov, Igor"https://zbmath.org/authors/?q=ai:novosselov.igorSummary: Electrohydrodynamic (EHD) thrust is produced when ionized fluid is accelerated in an electric field due to the momentum transfer between the charged species and neutral molecules. We extend the previously reported analytical model that couples space charge, electric field and momentum transfer to derive thrust force in one-dimensional planar coordinates. The electric current density in the model can be expressed in the form of Mott-Gurney law. After the correction for the drag force, the EHD thrust model yields good agreement with the experimental data from several independent studies. The EHD thrust expression derived from the first principles can be used in the design of propulsion systems and can be readily implemented in the numerical simulations.A nonlinear moment model for radiative transfer equationhttps://zbmath.org/1472.780152021-11-25T18:46:10.358925Z"Li, Ruo"https://zbmath.org/authors/?q=ai:li.ruo"Song, Peng"https://zbmath.org/authors/?q=ai:song.peng"Zheng, Lingchao"https://zbmath.org/authors/?q=ai:zheng.lingchaoNumerical simulation of formation and evolution of dissipative breathers of the classical Heisenberg antiferromagnet modelhttps://zbmath.org/1472.780302021-11-25T18:46:10.358925Z"Muminov, Kh. Kh."https://zbmath.org/authors/?q=ai:muminov.kh-kh"Muhamedova, Sh. F."https://zbmath.org/authors/?q=ai:muhamedova.sh-fSummary: In the present paper we conduct numerical simulation of the breather (soliton-like) solutions of classical Heisenberg antiferromagnetic acted upon by the variable external electromagnetic fields pumping and dissipation. The numerical recipe of simulation on the basic of stereographic projection is suggested avoiding singularities on the poles of the Bloch sphere. Parameters of regime of formation of dissipative breathers are determined.The appearance of particle tracks in detectorshttps://zbmath.org/1472.810112021-11-25T18:46:10.358925Z"Ballesteros, Miguel"https://zbmath.org/authors/?q=ai:ballesteros.miguel"Benoist, Tristan"https://zbmath.org/authors/?q=ai:benoist.tristan"Fraas, Martin"https://zbmath.org/authors/?q=ai:fraas.martin"Fröhlich, Jürg"https://zbmath.org/authors/?q=ai:frohlich.jurg-martinEver since its observation the seemingly innocuous appearance of the atomic particle tracks in detectors has puzzled the physicists as one of the most striking manifestations of the weird properties of the quantum world. To make a long story short, in the quoted words of M.\ Born at the 1927 Solvay conference: ``If one associates a spherical wave with each emission process, how can one understand that the track of each \(\alpha\)-particle appears as a (very nearly) straight line? In other words: how can the corpuscular character of the phenomenon be reconciled here with the representation by waves?'' In particular, the \(S\)-wave of the outgoing \(\alpha\)-particle is spherically symmetric, but the particle tracks are not. How is, then, that this initial symmetry is broken? In a sense the typical answer -- given in a celebrated W.\ Heisenberg 1927 thought experiment -- is well known: it is an effect of the collapse of the wave packet due to the (repeated) measurements of the particle position. But this is famously an answer that begs a lot of explanation and that, ever since its formulation, has elicited heated discussions not to be summarized here.
Admittedly however the present paper deals neither with a physical model for the atom ionization and the subsequent drop formation in a cloud chamber (along the lines, for example, of the quoted N.F.\ Mott 1929 paper), nor with an explanation of the strange nature of the quantum measurements, so that in particular no new insight is to be found about the wave packet collapse, or the \textit{Heisenberg cut}, notions that are simply accepted and used along the paper. For instance, in the words of the authors (page 438): ``To describe the effect of an instantaneous measurement of the approximate position of the particle on its state we follow the conventional wisdom of quantum mechanics: In the course of such a measurement whose result is given by some vector \(\mathbf q\in\mathbb{R}^d\), the state \(\rho\) of the particle changes according to'' the usual quantum rule of the wave packet collapse summarized in the subsequent equation (29). The focus of the discussion instead is to ``present a mathematically rigorous analysis of the appearance of particle tracks'' within the framework of the said ``conventional wisdom of quantum mechanics,'' namely to show that the track appearance is well accounted for with a scrupulous application of the quantum formalism. This is in any case a commendable task, and not a very easy one to carry out as the complexity of the subsequent discussion shows.
More precisely the authors want to ``present a theoretical analysis of a gedanken experiment of the sort Heisenberg had in mind in 1927,'' with repeated position measurements every \(\tau\) seconds. In their discussion however they do not deal with \textit{idealized} quantum measurements, but they take instead the considerable trouble of discussing the case of \textit{approximate} measurements. The general states of the charged particle of mass \(M\) are here density operators \(\rho\) in a Hilbert space \(\mathcal H\) where \(\mathbf X, \mathbf P\) are the position and momentum operators, while the state vectors \(\Omega\) of the electromagnetic (EM) field plus photomultipliers live in another Hilbert space \(\mathfrak H\). The values \(\mathbf q\in\mathbb{R}^d\) (representing the approximate position measurements) of suitable operators \(\mathbf Q\) in \(\mathfrak H\) are then ``supposed to be tightly correlated with the positions, \(\mathbf x\in\mathbb{R}^d\), of the charged particle.''
Before each measurement the EM field and photomultipliers always are in the state \(\Omega_{in}\); then during the light-scattering the state changes according to a propagator \(U_t(\mathbf x)\) (\(\mathbf x\) being the position of the charged particle during the scattering process, and \(t\ll\tau\) the scattering time span) and quickly relaxes back to \(\Omega_{in}\) long before the subsequent measurement is performed. It is therefore possible to define the transition amplitude \(V_{\mathbf q}(\mathbf x)\) of equation (7) representing the probability density amplitude of finding \(\mathbf q\) when the particle is in \(\mathbf x\). The operators \(V_{\mathbf q}(\mathbf X)\) will then constitute a positive-operator-valued measure (POVM) that turns out to be instrumental to implement the wave packet reduction of every approximate position measurement. On the other hand the evolution between two measurements of the position-momentum pair \(\mathbf X,\mathbf P\) of the freely moving particle is described by a propagator \(U_S\) associated to a symplectic matrix \(S\) in the phase space \(\Gamma\)
With the Gaussian \textit{ansatz} of equation (9) for the transition amplitude, a sequence of approximate measurements \(\mathbf q_0,\dots,\mathbf q_n\) falling in the subsets \(\Delta_0,\dots,\Delta_n\) entails a change in the initial density matrix \(\rho\) produced by a total operator \(W_n(\mathbf q_0,\dots,\mathbf q_n)= U_{S^{n+1}}V_{\mathbf q_n} (\mathbf X_{n\tau}) \ldots V_{\mathbf q_0} (\mathbf X)\) given as a repeated combination of \(V_{\mathbf q}\) and \(S\). Finally this gives rise to a probability measure \(\mathbb P_\rho\) on the process of the sequences \(\mathbf q_n\) that can be used to calculate the probability that the position of the particle at the times \(n\tau\) is within \(\Delta_n\). The aim of the paper now is to show that (page 435) ``with high probability, the cells \(\Delta_0,\dots,\Delta_n\) which indicate the positions of the particle at times \(0, \tau,\dots , n\tau\) , are centered in points ``close'' to \(\mathbf x(0), \mathbf x(\tau), \dots , \mathbf x(n\tau)\), respectively, where \(\mathbf x(t) =\mathbf x+t\mathbf v, t \in [0, n\tau]\), is the trajectory of a freely moving classical particle.'' Here \(\mathbf v\) is a value of \(\mathbf V=\mathbf P/M\)
Without retracing in this short review all the details of their exhaustive discussion we will only recall next that the authors on the one hand study (by means of a suitable family of coherent states \(|W,\zeta\rangle \) centered around phase space points \(\zeta\in\Gamma\)) ``the stochastic dynamics of a (quasi-) freely moving quantum particle subjected to repeated measurements of its approximate position;'' and on the other they ``introduce a stochastic process [equation (39)] with values in the classical phase space of the particle that indexes the trajectory of coherent states occupied by the particle under the forward dynamics.'' Their first main result is then summarized in the Theorem 2.2 that ``relates the sequence of measurement data of approximate particle positions to the sequence of phase space points determined by the stochastic process in Eq. (39)'' by establishing an equality in law between the classical positions \(\xi_n\) of the particle -- plus an independent Gaussian noise \(\eta_n\) -- and the measurement results \(\mathbf Q_n\). In the Theorem 2.4 they next ``determine the best guess of the initial condition of a phase space trajectory of the stochastic process introduced in (39) from its tail,'' and finally the Theorem 2.8 ``relates the positive operator-valued measure (POVM) induced by sequences of approximate particle position measurements to a POVM taking values in the space of coherent states.'' The bulk of the paper is thereafter devoted to a long and rather convoluted sequence of technical arguments peppered with a great deal of lemmas and propositions needed to prove the said results, and ends finally with a few examples of free particles, harmonic oscillators and particles in a constant magnetic field to show the efficacity of the method.Multipartite entanglement transfer in spin chainshttps://zbmath.org/1472.810262021-11-25T18:46:10.358925Z"Apollaro, Tony J. G."https://zbmath.org/authors/?q=ai:apollaro.tony-john-george"Sanavio, Claudio"https://zbmath.org/authors/?q=ai:sanavio.claudio"Chetcuti, Wayne Jordan"https://zbmath.org/authors/?q=ai:chetcuti.wayne-jordan"Lorenzo, Salvatore"https://zbmath.org/authors/?q=ai:lorenzo.salvatoreSummary: We investigate the transfer of genuine multipartite entanglement across a spin-\(\frac{1}{2}\) chain with nearest-neighbour \(XX\)-type interaction. We focus on the perturbative regime, where a block of spins is weakly coupled at each edge of a quantum wire, embodying the role of a multiqubit sender and receiver, respectively. We find that high-quality multipartite entanglement transfer is achieved at the same time that three excitations are transferred to the opposite edge of the chain. Moreover, we find that both a finite concurrence and tripartite negativity is attained at much shorter time, making \textit{GHZ}-distillation protocols feasible. Finally, we investigate the robustness of our protocol with respect to non-perturbative couplings and increasing lengths of the quantum wire.True spin and pseudo spin entanglement around Dirac points in graphene with Rashba spin-orbit interactionhttps://zbmath.org/1472.810302021-11-25T18:46:10.358925Z"Liu, Zheng"https://zbmath.org/authors/?q=ai:liu.zheng.1|liu.zheng.2|liu.zheng|liu.zheng.3"Zhang, Chao"https://zbmath.org/authors/?q=ai:zhang.chao.7"Cao, J. C."https://zbmath.org/authors/?q=ai:cao.juncheng|cao.jichaoSummary: We analytically obtained the Schmidt decomposition of the entangled state between the pseudo spin and the true spin in graphene with Rashba spin-orbit coupling. The entangled state has the standard form of the Bell state, where the SU(2) spin symmetry is broken. These states can be explicitly expressed as the superposition of two nonorthogonal, but mirror symmetrical spin states entangled with the pseudo spin states. Because of the closely locking between the pseudo spin and the true spin, it is found that the orbit curve in the spin-polarization parameter space for the fixed equi-energy contour around Dirac points has the same shape as the \(\delta \overrightarrow{k}\)-contour. Due to the spin-orbit coupling that cause the topological transition in the local geometry of the dispersion relation, the new equi-energy contours around the new emergent Dirac Points can be obtained by squeezing the one around the original Dirac point. The spin texture in the momentum space around the Dirac points is analyzed under the Rashba spin-orbit interaction and it is found that the orientation of the spin polarization at each crystal momentum \(\overrightarrow{k}\) is independent of the Rashba coupling strength.Controlled quantum state transfer in \textit{XX} spin chains at the quantum speed limithttps://zbmath.org/1472.810372021-11-25T18:46:10.358925Z"Acosta Coden, D. S."https://zbmath.org/authors/?q=ai:acosta-coden.d-s"Gómez, S. S."https://zbmath.org/authors/?q=ai:gomez.s-s"Ferrón, A."https://zbmath.org/authors/?q=ai:ferron.a"Osenda, O."https://zbmath.org/authors/?q=ai:osenda.omarSummary: The Quantum Speed Limit (QSL) can be found in many different situations, in particular in the propagation of information through quantum spin chains. In homogeneous chains it implies that taking information from one extreme of the chain to the other will take a time \(O(N/2)\), where \(N\) is the chain length. Using Optimal Control Theory we design control pulses that achieve near perfect population transfer between the extremes of the chain at times on the order of \(N/2\). Our results show that the control pulses that govern the dynamical behavior of chains with different lengths are closely related. The pulses were constructed for control schemes involving one or two actuators in chains with exchange couplings without static disorder. Our results also show that the two actuator scheme is considerably more robust against the presence of static disorder than the scheme that uses just a single one.Rashba control to minimize circuit cost of quantum Fourier algorithm in ballistic nanowireshttps://zbmath.org/1472.810532021-11-25T18:46:10.358925Z"Homid, A. H."https://zbmath.org/authors/?q=ai:homid.ali-h"Sakr, M. R."https://zbmath.org/authors/?q=ai:sakr.m-r"Mohamed, A.-B. A."https://zbmath.org/authors/?q=ai:mohamed.abdel-baset-a"Abdel-Aty, M."https://zbmath.org/authors/?q=ai:abdelaty.m-a|abdel-aty.mahmoud"Obada, A.-S. F."https://zbmath.org/authors/?q=ai:obada.abdel-shafy-fahmySummary: The presented work provides a new prospective of quantum computer hardware development through ballistic nanowires with Rashba effect. We address Rashba effect as a possible mechanism to realize novel qubit gates in nanowires. We apply our results to the design of a new quantum circuit for Fourier algorithm, which shows an improved quantum cost in terms of the number of gates. The current system can be successfully implemented to increase the production of quantum computer experimentally thanks to the absence of impurities. The introduced circuit will enhance the scope of experimental and theoretical research for the realization of other quantum algorithms, such as phase estimation and Shor's algorithms.Quantum heat switch with multiple qubitshttps://zbmath.org/1472.810542021-11-25T18:46:10.358925Z"Jamshidi Farsani, Marzie"https://zbmath.org/authors/?q=ai:jamshidi-farsani.marzie"Fazio, Rosario"https://zbmath.org/authors/?q=ai:fazio.rosarioSummary: We further elaborate on the device proposed by rhe authors [Quantum Sci. Technol. 2, No. 4. Article ID 044007, pp. (2017; \url{doi:10.1088/2058-9565/aa8330})], in which coupled superconducting qubits can play the role of a quantum heat switch. In the present paper we analyze the performances of the switch if the number of qubits increases considering in details the cases of three and four qubits. To this aim we study the effect of the number of qubits on the transmitted power between baths. As the number of qubits increases, the transmitted power between baths increases as well.Measuring space deformation via graphene under constraintshttps://zbmath.org/1472.810762021-11-25T18:46:10.358925Z"Jellal, Ahmed"https://zbmath.org/authors/?q=ai:jellal.ahmedSummary: We describe the lattice deformation in graphene under strain effect by considering the spacial-momenta coordinates do not commute. This later can be realized by introducing the star product to end up with a generalized Heisenberg algebra. Within such framework, we build a new model describing Dirac fermions interacting with an external source that is noncommutative parameter \(\kappa\) dependent. The solutions of energy spectrum are showing Landau levels in similar way to the case of a real magnetic field applied to graphene. We show that some strain configurations can be used to explicitly evaluate \(\kappa\) and then offer a piste toward its measurement.Ground states for a linearly coupled indefinite Schrödinger system with steep potential wellhttps://zbmath.org/1472.810802021-11-25T18:46:10.358925Z"Lin, Ying-Chieh"https://zbmath.org/authors/?q=ai:lin.ying-chieh"Wang, Kuan-Hsiang"https://zbmath.org/authors/?q=ai:wang.kuan-hsiang"Wu, Tsung-fang"https://zbmath.org/authors/?q=ai:wu.tsungfangSummary: In this paper, we study a class of linearly coupled Schrödinger systems with steep potential wells, which arises from Bose-Einstein condensates. The existence of positive ground states is investigated by exploiting the relation between the Nehari manifold and fiberring maps. Some interesting phenomena are that we do not need the weight functions in the nonlinear terms to be integrable or bounded and we can relax the upper control condition of the coupling function. Moreover, the decay rate and concentration phenomenon of positive ground states are also studied.
{\copyright 2021 American Institute of Physics}Heun operator of Lie type and the modified algebraic Bethe ansatzhttps://zbmath.org/1472.810912021-11-25T18:46:10.358925Z"Bernard, Pierre-Antoine"https://zbmath.org/authors/?q=ai:bernard.pierre-antoine"Crampé, Nicolas"https://zbmath.org/authors/?q=ai:crampe.nicolas"Shaaban Kabakibo, Dounia"https://zbmath.org/authors/?q=ai:shaaban-kabakibo.dounia"Vinet, Luc"https://zbmath.org/authors/?q=ai:vinet.lucSummary: The generic Heun operator of Lie type is identified as a certain \textit{BC}-Gaudin magnet Hamiltonian in a magnetic field. By using the modified algebraic Bethe ansatz introduced to diagonalize such Gaudin models, we obtain the spectrum of the generic Heun operator of Lie type in terms of the Bethe roots of inhomogeneous Bethe equations. We also show that these Bethe roots are intimately associated with the roots of polynomial solutions of the differential Heun equation. We illustrate the use of this approach in two contexts: the representation theory of \(O(3)\) and the computation of the entanglement entropy for free Fermions on the Krawtchouk chain.
{\copyright 2021 American Institute of Physics}A new spectral analysis of stationary random Schrödinger operatorshttps://zbmath.org/1472.810922021-11-25T18:46:10.358925Z"Duerinckx, Mitia"https://zbmath.org/authors/?q=ai:duerinckx.mitia"Shirley, Christopher"https://zbmath.org/authors/?q=ai:shirley.christopherThe authors consider random Schrödinger operators of the form
\[
-\Delta + \lambda V_{\omega}
\]
and the associated Schrödinger equation, where \(V_{\omega}\) is a realization of a stationary random potential \(V\). The regime under consideration here is \(0<\lambda \ll 1\). The main goal of the authors is to develop a spectral approach to describe the long time behavior of the system beyond perturbative timescales by using ideas from Malliavin calculus, leading to rigorous Mourre type results. In particular, the authors describe the dynamics by a fibered family of spectral perturbation problems. They then state a number of exact resonance conjectures which would require that Bloch waves exist as resonant modes. An approximate resonance result is obtained and the first spectral proof of the decay of time correlations on the kinetic timescale is also provided.Diffeomorphism groups in quantum theory and statistical physicshttps://zbmath.org/1472.811142021-11-25T18:46:10.358925Z"Goldin, Gerald A."https://zbmath.org/authors/?q=ai:goldin.gerald-aSummary: Symmetry groups describe invariances or partial invariances in physical systems under transformations. Locality refers to the association between physical effects and spatial or spacetime regions, with ``action at a distance'' forbidden. Local symmetry joins these ideas mathematically in the theory of certain infinite-dimensional groups and their representations. This chapter is an extended abstract of lectures by the author, surveying how unitary representations of diffeomorphism groups and the corresponding current algebras provide a unifying framework for understanding or predicting a wide variety of different quantum and statistical systems.
For the entire collection see [Zbl 1472.53006].Spinorial \(R\) operator and algebraic Bethe ansatzhttps://zbmath.org/1472.811202021-11-25T18:46:10.358925Z"Karakhanyan, D."https://zbmath.org/authors/?q=ai:karakhanyan.david"Kirschner, R."https://zbmath.org/authors/?q=ai:kirschner.rolandSummary: We propose a new approach to the spinor-spinor R-matrix with orthogonal and symplectic symmetry. Based on this approach and the fusion method we relate the spinor-vector and vector-vector monodromy matrices for quantum spin chains. We consider the explicit spinor \(R\) matrices of low rank orthogonal algebras and the corresponding \(RTT\) algebras. Coincidences with fundamental \(R\) matrices allow to relate the Algebraic Bethe Ansatz for spinor and vector monodromy matrices.Finite volume effects on chiral phase transition and pseudoscalar mesons properties from the Polyakov-Nambu-Jona-Lasinio modelhttps://zbmath.org/1472.811592021-11-25T18:46:10.358925Z"Zhao, Ya-Peng"https://zbmath.org/authors/?q=ai:zhao.ya-peng"Yin, Pei-Lin"https://zbmath.org/authors/?q=ai:yin.pei-lin"Yu, Zhen-Hua"https://zbmath.org/authors/?q=ai:yu.zhenhua"Zong, Hong-Shi"https://zbmath.org/authors/?q=ai:zong.hongshiSummary: Within the framework of Polyakov-Nambu-Jona-Lasinio model and by means of Multiple Reflection Expansion, we study the finite volume effects on chiral phase transition, especially its influence on the location of the possible critical end point (CEP) and masses of mesons. Our result shows that as the radius of the sphere decreases, the location of CEP shifts toward smaller temperature while remains almost a constant in chemical potential. As for the finite volume effects on the masses of mesons, the masses of \(\pi\) and \(K\) increase with decreasing volume, while for \(\sigma\), \(\eta\) and \(\eta^\prime\) the situation is the opposite. Especially, the masses of chiral parters \(\pi\) and \(\sigma\) get closer as the volume decreases, indicating that the dynamical chiral symmetry breaking effect reduces with decreasing volume.Two faces of Douglas-Kazakov transition: from Yang-Mills theory to random walks and beyondhttps://zbmath.org/1472.811652021-11-25T18:46:10.358925Z"Gorsky, Alexander"https://zbmath.org/authors/?q=ai:gorskii.aleksander-sergeevich"Milekhin, Alexey"https://zbmath.org/authors/?q=ai:milekhin.alexey"Nechaev, Sergei"https://zbmath.org/authors/?q=ai:nechaev.sergei-konstantinovichSummary: Being inspired by the connection between 2D Yang-Mills (YM) theory and (1+1)D ``vicious walks'' (VW), we consider different incarnations of large-\(N\) Douglas-Kazakov (DK) phase transition in gauge field theories and stochastic processes focusing at possible physical interpretations. We generalize the connection between YM and VW, study the influence of initial and final distributions of walkers on the DK phase transition, and describe the effect of the \(\theta\)-term in corresponding stochastic processes. We consider the Jack stochastic process involving Calogero-type interaction between walkers and investigate the dependence of DK transition point on a coupling constant. Relying on the relation between large-\(N 2\) D \(q\)-YM and extremal black hole (BH) with large-\(N\) magnetic charge, we speculate about a physical interpretation of a DK phase transitions in a 4D extremal charged BH.Chiral anomaly in Weyl systems: no violation of classical conservation lawshttps://zbmath.org/1472.811692021-11-25T18:46:10.358925Z"Morawetz, K."https://zbmath.org/authors/?q=ai:morawetz.klausSummary: The anomalous term \(\sim \mathbf{EB}\) in the balance of the chiral density can be rewritten as quantum current in the classical balance of density. Therefore it does not violate conservation laws as sometimes claimed to be caused by quantum fluctuations.The cubic fixed point at large \(N\)https://zbmath.org/1472.811752021-11-25T18:46:10.358925Z"Binder, Damon J."https://zbmath.org/authors/?q=ai:binder.damon-jSummary: By considering the renormalization group flow between \(N\) coupled Ising models in the UV and the cubic fixed point in the IR, we study the large \(N\) behavior of the cubic fixed points in three dimensions. We derive a diagrammatic expansion for the \(1/N \) corrections to correlation functions. Leading large \(N\) corrections to conformal dimensions at the cubic fixed point are then evaluated using numeric conformal bootstrap data for the 3d Ising model.Holographic unitary renormalization group for correlated electrons. II: Insights on fermionic criticalityhttps://zbmath.org/1472.811762021-11-25T18:46:10.358925Z"Mukherjee, Anirban"https://zbmath.org/authors/?q=ai:mukherjee.anirban"Lal, Siddhartha"https://zbmath.org/authors/?q=ai:lal.siddharthaSummary: Capturing the interplay between electronic correlations and many-particle entanglement requires a unified framework for Hamiltonian and eigenbasis renormalization. In this work, we apply the unitary renormalization group (URG) scheme developed in a companion work [the authors, ibid. 960, Article ID 115170, 72 p. (2020; Zbl 1472.81177)] to the study of two archetypal models of strongly correlated lattice electrons, one with translation invariance and one without. We obtain detailed insight into the emergence of various gapless and gapped phases of quantum electronic matter by computing effective Hamiltonians from numerical evaluation of the various RG equations, as well as their entanglement signatures through their respective tensor network descriptions. For the translationally invariant model of a single-band of interacting electrons, this includes results on gapless metallic phases such as the Fermi liquid and Marginal Fermi liquid, as well as gapped phases such as the reduced Bardeen-Cooper-Schrieffer, pair density-wave and Mott liquid phases. Additionally, a study of a generalised Sachdev-Ye model with disordered four-fermion interactions offers detailed results on many-body localised phases, as well as thermalised phase. We emphasise the distinctions between the various phases based on a combined analysis of their dynamical (obtained from the effective Hamiltonian) and entanglement properties. Importantly, the RG flow of the Hamiltonian vertex tensor network is shown to lead to emergent gauge theories for the gapped phases. Taken together with results on the holographic spacetime generated from the RG of the many-particle eigenstate (seen through, for instance, the holographic upper bound of the one-particle entanglement entropy), our analysis offer an ab-initio perspective of the gauge-gravity duality for quantum liquids that are emergent in systems of correlated electrons.Infrared duality in unoriented pseudo del Pezzohttps://zbmath.org/1472.812022021-11-25T18:46:10.358925Z"Antinucci, Andrea"https://zbmath.org/authors/?q=ai:antinucci.andrea"Mancani, Salvo"https://zbmath.org/authors/?q=ai:mancani.salvo"Riccioni, Fabio"https://zbmath.org/authors/?q=ai:riccioni.fabioSummary: We study the orientifold projections of the \(\mathcal{N} = 1\) superconformal field theories describing D3-branes probing the Pseudo del Pezzo singularities \(\mathrm{PdP}_{3b}\) and \(\mathrm{PdP}_{3c}\). The \(\mathrm{PdP}_{3c}\) parent theory admits two inequivalent orientifolds. Exploiting \(a\) maximization, we find that one of the two has an \(a\)-charge smaller than what one would expect from the orientifold projection, which suggests that the theory flows to the fixed point in the infrared. Surprisingly, the value of \(a\) coincides with the charge of the unoriented \(\mathrm{PdP}_{3b}\) and we interpret this as the sign of an infrared duality.On the empirical consequences of the AdS/CFT dualityhttps://zbmath.org/1472.812042021-11-25T18:46:10.358925Z"Dardashti, Radin"https://zbmath.org/authors/?q=ai:dardashti.radin"Dawid, Richard"https://zbmath.org/authors/?q=ai:dawid.richard"Gryb, Sean"https://zbmath.org/authors/?q=ai:gryb.sean"Thébault, Karim"https://zbmath.org/authors/?q=ai:thebault.karim-p-ySummary: We provide an analysis of the empirical consequences of the AdS/CFT duality with reference to the application of the duality in a fundamental theory, effective theory, and instrumental context. Analysis of the first two contexts is intended to serve as a guide to the potential empirical and ontological status of gauge/gravity dualities as descriptions of actual physics at the Planck scale. The third context is directly connected to the use of AdS/CFT to describe real quark-gluon plasmas. In the latter context, we find that neither of the two duals are confirmed by the empirical data.
For the entire collection see [Zbl 1460.81001].Qubit construction in 6D SCFTshttps://zbmath.org/1472.812202021-11-25T18:46:10.358925Z"Heckman, Jonathan J."https://zbmath.org/authors/?q=ai:heckman.jonathan-jSummary: We consider a class of 6D superconformal field theories (SCFTs) which have a large \(N\) limit and a semi-classical gravity dual description. Using the quiver-like structure of 6D SCFTs we study a subsector of operators protected from large operator mixing. These operators are characterized by degrees of freedom in a one-dimensional spin chain, and the associated states are generically highly entangled. This provides a concrete realization of qubit-like states in a strongly coupled quantum field theory. Renormalization group flows triggered by deformations of 6D UV fixed points translate to specific deformations of these one-dimensional spin chains. We also present a conjectural spin chain Hamiltonian which tracks the evolution of these states as a function of renormalization group flow, and study qubit manipulation in this setting. Similar considerations hold for theories without \(AdS\)duals, such as 6D little string theories and 4D SCFTs obtained from compactification of the partial tensor branch theory on a \(T^2\).Post-quench evolution of complexity and entanglement in a topological systemhttps://zbmath.org/1472.812292021-11-25T18:46:10.358925Z"Ali, Tibra"https://zbmath.org/authors/?q=ai:ali.tibra"Bhattacharyya, Arpan"https://zbmath.org/authors/?q=ai:bhattacharyya.arpan"Shajidul Haque, S."https://zbmath.org/authors/?q=ai:shajidul-haque.s"Kim, Eugene H."https://zbmath.org/authors/?q=ai:kim.eugene-h"Moynihan, Nathan"https://zbmath.org/authors/?q=ai:moynihan.nathanSummary: We investigate the evolution of complexity and entanglement following a quench in a one-dimensional topological system, namely the Su-Schrieffer-Heeger model. We demonstrate that complexity can detect quantum phase transitions and shows signatures of revivals; this observation provides a practical advantage in information processing. We also show that the complexity saturates much faster than the entanglement entropy in this system, and we provide a physical argument for this. Finally, we demonstrate that complexity is a less sensitive probe of topological order, compared with measures of entanglement.Casimir force and its effects on pull-in instability modelled using molecular dynamics simulationshttps://zbmath.org/1472.812342021-11-25T18:46:10.358925Z"Sircar, Avirup"https://zbmath.org/authors/?q=ai:sircar.avirup"Patra, Puneet Kumar"https://zbmath.org/authors/?q=ai:patra.puneet-kumar"Batra, Romesh C."https://zbmath.org/authors/?q=ai:batra.romesh-cSummary: We present a new methodology to incorporate the Casimir forces within the molecular dynamics (MD) framework. At atomistic scales, the potential energy between two particles arising due to the Casimir effect can be represented as \(U(r_{ij}) = C/r^7\). Incorporating the Casimir effect in MD simulations requires the knowledge of \(C\), a problem hitherto unsolved. We overcome this by equating the total potential energy contributions due to each atomistic pair with the potential energy of continuum scale interacting bodies having similar geometries. After having identified the functional form of \(C\), standard MD simulations are augmented with the potential energy contribution due to pairwise Casimir interactions. The developed framework is used to study effects of the Casimir force on the pull-in instability of rectangular and hollow cylindrical shaped deformable electrodes separated by a small distance from a fixed substrate electrode. Our MD results for pull-instability qualitatively agree with the previously reported analytical results but are quantitatively different. The effect of using longer-ranged Casimir forces in a constant temperature environment on the pull-in behaviour has also been studied.Supersymmetric indices on \(I \times T^2\), elliptic genera and dualities with boundarieshttps://zbmath.org/1472.812452021-11-25T18:46:10.358925Z"Sugiyama, Katsuyuki"https://zbmath.org/authors/?q=ai:sugiyama.katsuyuki"Yoshida, Yutaka"https://zbmath.org/authors/?q=ai:yoshida.yutakaSummary: We study three dimensional \(\mathcal{N} = 2\) supersymmetric theories on \(I \times M_2\) with 2d \(\mathcal{N} = (0, 2)\) boundary conditions at the boundaries \(\partial(I \times M_2) = M_2 \sqcup M_2\), where \(M_2 = \mathbb{C}\) or \(T^2\). We introduce supersymmetric indices of three dimensional \(\mathcal{N} = 2\) theories on \(I \times T^2\) that couple to elliptic genera of 2d \(\mathcal{N} = (0, 2)\) theories at the two boundaries. We evaluate the \(I \times T^2\) indices in terms of supersymmetric localization and study dualities on the \(I \times M_2\). We consider the dimensional reduction of \(I \times T^2\) to \(I \times S^1\) and obtain the localization formula of 2d \(\mathcal{N} = (2, 2)\) supersymmetric indices on \(I \times S^1\). We illustrate computations of open string Witten indices based on gauged linear sigma models. Correlation functions of Wilson loops on \(I \times S^1\) agree with Euler pairings in the geometric phase and also agree with cylinder amplitudes for B-type boundary states of Gepner models in the Landau-Ginzburg phase.Configuration entropy description of charmonium dissociation under the influence of magnetic fieldshttps://zbmath.org/1472.812682021-11-25T18:46:10.358925Z"Braga, Nelson R. F."https://zbmath.org/authors/?q=ai:braga.nelson-r-f"da Mata, Rodrigo"https://zbmath.org/authors/?q=ai:da-mata.rodrigoSummary: Heavy ion collisions, produced in particle accelerators, lead to the formation of a new state of matter, known as the quark gluon plasma. It is not possible to observe directly the plasma, where quarks and gluons are not confined into hadrons. All the available information comes from the particles that reach the detectors after the strongly interacting matter hadronizes. Among those particles, one that plays an important role is the charmonium \(\mathrm{J}/\psi\) heavy meson, made of a \(c \bar{c}\) quark anti-quark pair. The fraction of such particles produced in a heavy ion collision is related to the dissociation level caused by the plasma. On the other hand, the dissociation of \(J/\Psi\) in the plasma is influenced by the temperature and the density of the medium and also by the presence of magnetic fields, that are produced in non central collisions. A very interesting tool to study stability of physical systems is the configuration entropy (CE). In recent years many examples in various kinds of physical systems appeared in the literature, where an increase in the CE is associated with an increase in the instability of the system. In this letter we calculate the CE for charmonium quasistates inside a plasma with a magnetic field background, in order to investigate how the instability, corresponding in this case to the dissociation in the thermal medium, is translated into the dependence of the CE on the field.Covariant kinetic theory and transport coefficients for Gribov plasmahttps://zbmath.org/1472.812722021-11-25T18:46:10.358925Z"Jaiswal, Amaresh"https://zbmath.org/authors/?q=ai:jaiswal.amaresh"Haque, Najmul"https://zbmath.org/authors/?q=ai:haque.najmulSummary: Gribov quantization is a method to improve the infrared dynamics of Yang-Mills theory. We study the thermodynamics and transport properties of a plasma consisting of gluons whose propagator is improved by the Gribov prescription. We first construct thermodynamics of Gribov plasma using the gauge invariant Gribov dispersion relation for interacting gluons. When the Gribov parameter in the dispersion relation is temperature dependent, one expects a mean field correction to the Boltzmann equation. We formulate covariant kinetic theory for the Gribov plasma and determine the mean-field contribution in the Boltzmann equation. This leads to a quasiparticle like framework with a bag correction to pressure and energy density which mimics confinement. The temperature dependence of the Gribov parameter and bag pressure is fixed by matching with lattice results for a system of gluons. Finally we calculate the temperature dependence of the transport coefficients, i.e., bulk and shear viscosities.Heavy quarkonium in extreme conditionshttps://zbmath.org/1472.812762021-11-25T18:46:10.358925Z"Rothkopf, Alexander"https://zbmath.org/authors/?q=ai:rothkopf.alexanderSummary: In this report we review recent progress achieved in the understanding of heavy quarkonium under extreme conditions from a theory perspective. Its focus lies both on quarkonium properties in thermal equilibrium, as well as recent developments towards a genuine real-time description, valid also out-of-equilibrium. We will give an overview of the theory tools developed and deployed over the last decade, including effective field theories, lattice field theory simulations, modern methods for spectral reconstructions and the open quantum systems paradigm. The report will discuss in detail the concept of quarkonium melting, providing the reader with a contemporary perspective. In order to judge where future progress is needed we will also discuss recent results from experiments and phenomenological modeling of quarkonium in relativistic heavy-ion collisions.Back reaction effects on the imaginary potential of quarkonia in heavy quark cloudhttps://zbmath.org/1472.812782021-11-25T18:46:10.358925Z"Wu, Ping-ping"https://zbmath.org/authors/?q=ai:wu.pingping"Zhu, Xiangrong"https://zbmath.org/authors/?q=ai:zhu.xiangrong"Zhang, Zi-qiang"https://zbmath.org/authors/?q=ai:zhang.ziqiangSummary: Applying the AdS/CFT correspondence, we investigate the effect of back reaction on the imaginary part of heavy quarkonia potential in strongly coupled \(\mathcal{N} = 4\) supersymmetric Yang-Mills (SYM) plasma. The back reaction considered here arises from the inclusion of static heavy quarks uniformly distributed over \(\mathcal{N} = 4\) SYM plasma. It is shown that the presence of back reaction reduces the absolute value of the imaginary potential thus decreasing the thermal width. Furthermore, the results imply that back reaction enhances the quarkonia dissociation.Exchange interactions, Yang-Baxter relations and transparent particleshttps://zbmath.org/1472.813062021-11-25T18:46:10.358925Z"Polychronakos, Alexios P."https://zbmath.org/authors/?q=ai:polychronakos.alexios-pSummary: We introduce a class of particle models in one dimension involving exchange interactions that have scattering properties satisfying the Yang-Baxter consistency condition. A subclass of these models exhibits reflectionless scattering, in which particles are ``transparent'' to each other, generalizing a property hitherto only known for the exchange Calogero model. The thermodynamics of these systems can be derived using the asymptotic Bethe-Ansatz method.Spin texture and Berry phase for heavy-mass holes confined in SiGe mixed-alloy two-dimensional system: intersubband interaction via the coexistence of Rashba and Dresselhaus spin-orbit interactionshttps://zbmath.org/1472.813172021-11-25T18:46:10.358925Z"Tojo, Tatsuki"https://zbmath.org/authors/?q=ai:tojo.tatsuki"Takeda, Kyozaburo"https://zbmath.org/authors/?q=ai:takeda.kyozaburoSummary: By extending the \(\boldsymbol{k} \cdot \boldsymbol{p}\) approach, we study the spin texture and Berry phase of heavy-mass holes (HHs) confined in the SiGe two-dimensional (2D) quantum well system, focusing on the intersubband interaction via the coexistence of the Rashba and Dresselhaus spin-orbit interactions (SOIs). The coexistence of both SOIs generates spin-stabilized(+)/destabilized(-) HHs. The strong intersubband interaction causes \textit{quasi}-degenerate states resembling the 2D massive Dirac fermion. Consequently, the Berry phases of HHs have unique energy dependence understood by counting the \textit{quasi}-degenerate points with the signs of the Berry phases. Thermal averaging of the Berry phase demonstrates that HH\(+/-\) has a peculiar plateau of \(+\pi/-\pi\) at less than 30 K and then changes its sign at approximately 200 K.The intrinsical character of the electronic correlation in an electron gashttps://zbmath.org/1472.813242021-11-25T18:46:10.358925Z"Liu, Yu-Liang"https://zbmath.org/authors/?q=ai:liu.yuliangSummary: By introducing the phase transformation of electron operators, we map the equation of motion of an one-particle Green's function into that of a non-interacting one-particle Green's function where the electrons are moving in a time-depending scalar potential and pure gauge fields for a D-dimensional electron gas, and we demonstrate that the electronic correlation strength strongly depends upon the excitation energy spectrum and collective excitation modes of electrons. It naturally explains that the electronic correlation strength is strong in the one dimension, while it is weak in the three dimensions.Diagonal entropy in many-body systems: volume effect and quantum phase transitionshttps://zbmath.org/1472.813252021-11-25T18:46:10.358925Z"Wang, Zhengan"https://zbmath.org/authors/?q=ai:wang.zhengan"Sun, Zheng-Hang"https://zbmath.org/authors/?q=ai:sun.zheng-hang"Zeng, Yu"https://zbmath.org/authors/?q=ai:zeng.yu.1"Lang, Haifeng"https://zbmath.org/authors/?q=ai:lang.haifeng"Hong, Qiantan"https://zbmath.org/authors/?q=ai:hong.qiantan"Cui, Jian"https://zbmath.org/authors/?q=ai:cui.jian"Fan, Heng"https://zbmath.org/authors/?q=ai:fan.hengSummary: We investigate the diagonal entropy(DE) of the ground state for quantum many-body systems, including the XY model and the Ising model with next nearest neighbor interactions. We focus on the DE of a subsystem of \(L\) continuous spins. We show that the DE in many-body systems, regardless of integrability, can be represented as a volume term plus a logarithmic correction and a constant offset. Quantum phase transition points can be explicitly identified by the three coefficients thereof. Besides, by combining entanglement entropy and the relative entropy of quantum coherence, as two celebrated representatives of quantumness, we simply obtain the DE, which naturally has the potential to reveal the information of quantumness. More importantly, the DE is concerning only the diagonal form of the ground state reduced density matrix, making it feasible to measure in real experiments, and therefore it has immediate applications in demonstrating quantum supremacy on state-of-the-art quantum simulators.On the effect of fractional statistics on quantum ion acoustic waveshttps://zbmath.org/1472.813272021-11-25T18:46:10.358925Z"Ourabah, Kamel"https://zbmath.org/authors/?q=ai:ourabah.kamelSummary: In this paper, I study the effect of a small deviation from the Fermi-Dirac statistics on the quantum ion acoustic waves. For this purpose, a quantum hydrodynamic model is developed based on the Polychronakos statistics, which allows for a smooth interpolation between the Fermi and Bose limits, passing through the case of classical particles. The model includes the effect of pressure as well as quantum diffraction effects through the Bohm potential. The equation of state for electrons obeying fractional statistics is obtained and the effect of fractional statistics on the kinetic energy and the coupling parameter is analyzed. Through the model, the effect of fractional statistics on the quantum ion acoustic waves is highlighted, exploring both linear and weakly nonlinear regimes. It is found that fractional statistics enhance the amplitude and diminish the width of the quantum ion acoustic waves. Furthermore, it is shown that a small deviation from the Fermi-Dirac statistics can modify the type structures, from bright to dark soliton. All known results of fully degenerate and non-degenerate cases are reproduced in the proper limits.Finite temperature aspect ratio in ultra-cold Bose gas for large Nhttps://zbmath.org/1472.813292021-11-25T18:46:10.358925Z"Kouidri, S."https://zbmath.org/authors/?q=ai:kouidri.smaineSummary: We present a detailed study of the temperature dependence of the condensate fraction, collective excitation and aspect ratio profiles of a Bose-condensed gas in a harmonic trap for large numbers of condensate atoms up to 85000. These quantities are calculated self-consistently using the generalized Hartree-Fock-Bogoliubov (GHFB) equations. We determine the evolution of the aspect ratio at zero and finite temperature \textit{via} the condensed fraction. We compare our results with experimental data and we find a good agreement.Spin orbit coupled Bose Einstein condensate in a two dimensional bichromatic optical latticehttps://zbmath.org/1472.813302021-11-25T18:46:10.358925Z"Oztas, Z."https://zbmath.org/authors/?q=ai:oztas.zSummary: We numerically investigate the localization of Bose Einstein condensate (BEC) with spin orbit coupling in a two dimensional bichromatic optical lattice. We study localization in weakly interacting and non-interacting regimes. The existence of stationary localized states in the presence of spin-orbit and Rabi couplings has been confirmed. We find that spin orbit coupling favors localization, whereas Rabi coupling has a slight delocalization effect.Ground-state properties of dilute one-dimensional Bose gas with three-body repulsionhttps://zbmath.org/1472.813312021-11-25T18:46:10.358925Z"Pastukhov, Volodymyr"https://zbmath.org/authors/?q=ai:pastukhov.volodymyrSummary: We determined perturbatively the low-energy universal thermodynamics of dilute one-dimensional bosons with the three-body repulsive forces. The final results are presented for the limit of vanishing potential range in terms of three-particle scattering length. An analogue of Tan's energy theorem for considered system is derived in generic case without assuming weakness of the interparticle interaction. We also obtained an exact identity relating the three-body contact to the energy density.Soliton lattices in the Gross-Pitaevskii equation with nonlocal and repulsive couplinghttps://zbmath.org/1472.813322021-11-25T18:46:10.358925Z"Sakaguchi, Hidetsugu"https://zbmath.org/authors/?q=ai:sakaguchi.hidetsuguSummary: Spatially-periodic patterns are studied in nonlocally coupled Gross-Pitaevskii equation. We show first that spatially periodic patterns appear in a model with the dipole-dipole interaction. Next, we study a model with a finite-range coupling, and show that a repulsively coupled system is closely related with an attractively coupled system and its soliton solution becomes a building block of the spatially-periodic structure. That is, the spatially-periodic structure can be interpreted as a soliton lattice. An approximate form of the soliton is given by a variational method. Furthermore, the effects of the rotating harmonic potential and spin-orbit coupling are numerically studied.\(\mathcal{N} = 4\) supersymmetric U(2)-spin hyperbolic Calogero-Sutherland modelhttps://zbmath.org/1472.813332021-11-25T18:46:10.358925Z"Fedoruk, Sergey"https://zbmath.org/authors/?q=ai:fedoruk.sergeySummary: The \(\mathcal{N} = 4\) supersymmetric U(2)-spin hyperbolic Calogero-Sutherland model with odd matrix fields is examined. Explicit form of the \(\mathcal{N} = 4\) supersymmetry generators is derived. The Lax representation for the dynamics of the \(\mathcal{N} = 4\) hyperbolic U(2)-spin Calogero-Sutherland system is found. The reduction to the \(\mathcal{N} = 4\) supersymmetric spinless hyperbolic Calogero-Sutherland system is established.Graphene wormhole trapped by external magnetic fieldhttps://zbmath.org/1472.813352021-11-25T18:46:10.358925Z"Garcia, G. Q."https://zbmath.org/authors/?q=ai:garcia.gabriel-queiroz"Porfírio, P. J."https://zbmath.org/authors/?q=ai:porfirio.paulo-j"Moreira, D. C."https://zbmath.org/authors/?q=ai:moreira.d-c"Furtado, C."https://zbmath.org/authors/?q=ai:furtado.claudioSummary: In this work we study the behavior of massless fermions in a graphene wormhole and in the presence of an external magnetic field. The graphene wormhole is made from two sheets of graphene which play the roles of asymptotically flat spaces connected through a carbon nanotube with a zig-zag boundary. We solve the massless Dirac equation within this geometry, analyze the corresponding wave function, and show that the energy spectra of these solutions exhibit behavior similar to Landau levels.Strongly correlated Fermi systems. A new state of matterhttps://zbmath.org/1472.820012021-11-25T18:46:10.358925Z"Amusia, Miron"https://zbmath.org/authors/?q=ai:amusia.miron-ya"Shaginyan, Vasily"https://zbmath.org/authors/?q=ai:shaginyan.vasily-rThe book is devoted to properties of strongly correlated Fermi systems (SCFS), such as heavy fermion (HF) metals, quantum spin liquids, quasicrystals, and two-dimensional (2D) systems, which are considered as a new state of matter. The introduced new state of matter is obtained by demonstrating the universal behaviour of the thermodynamic, transport, and relaxation properties. The book presents theoretical evolutions with arguments based on experimental results that very different SCFC have a universal behaviour induced by fermion condensation quantum phase transition (FCQPT). The book discusses general mechanisms leading to the formation of flat bands and studies the common properties of SCFS. Moreover, the authors consider high-\(T_c\) superconductors within a coarse-grained model based on the FCQPT theory, to illuminate their generic relationship with HF metals. To show the ubiquitous features of FCQPT the authors consider its possible role in the emergence of the Universe. Using the model of a homogeneous HF liquid the universal behaviour of high-\(T_c\) superconductors, HF metals, quasicrystals, quantum spin liquids, and 1D and 2D Fermi systems at low temperatures are studied. Moreover, using the FCQPT theory the universal properties of HF compounds systems are discussed. The book contains many results which will be interesting for researchers in the field of condensed matters physics.Gaussian unitary ensembles with two jump discontinuities, PDEs, and the coupled Painlevé II and IV systemshttps://zbmath.org/1472.820022021-11-25T18:46:10.358925Z"Lyu, Shulin"https://zbmath.org/authors/?q=ai:lyu.shulin"Chen, Yang"https://zbmath.org/authors/?q=ai:chen.yang.1Summary: We consider the Hankel determinant generated by the Gaussian weight with two jump discontinuities. Utilizing the results of \textit{C. Min} and \textit{Y. Chen} [Math. Methods Appl. Sci. 42, No. 1, 301--321 (2019; Zbl 1409.33018)] where a second-order partial differential equation (PDE) was deduced for the log derivative of the Hankel determinant by using the ladder operators adapted to orthogonal polynomials, we derive the coupled Painlevé IV system which was established in [\textit{X.-B. Wu} and \textit{S.-X. Xu}, Nonlinearity 34, No. 4, 2070--2115 (2021; Zbl 1470.34238)] by a study of the Riemann-Hilbert problem for orthogonal polynomials. Under double scaling, we show that, as \(n \rightarrow \infty\), the log derivative of the Hankel determinant in the scaled variables tends to the Hamiltonian of a coupled Painlevé II system and it satisfies a second-order PDE. In addition, we obtain the asymptotics for the recurrence coefficients of orthogonal polynomials, which are connected with the solutions of the coupled Painlevé II system.Globe-hoppinghttps://zbmath.org/1472.820032021-11-25T18:46:10.358925Z"Chistikov, Dmitry"https://zbmath.org/authors/?q=ai:chistikov.dmitry-v"Goulko, Olga"https://zbmath.org/authors/?q=ai:goulko.olga"Kent, Adrian"https://zbmath.org/authors/?q=ai:kent.adrian"Paterson, Mike"https://zbmath.org/authors/?q=ai:paterson.mike-sSummary: We consider versions of the grasshopper problem
[the second and third author, Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 473, No. 2207, Article ID 20170494, 19 p. (2017; Zbl 1404.60025)]
on the circle and the sphere, which are relevant to Bell inequalities. For a circle of circumference \(2 \pi \), we show that for unconstrained lawns of any length and arbitrary jump lengths, the supremum of the probability for the grasshopper's jump to stay on the lawn is one. For antipodal lawns, which by definition contain precisely one of each pair of opposite points and have length \(\pi \), we show this is true except when the jump length \(\varphi\) is of the form \(\pi (p/q)\) with \(p, q\) coprime and \(p\) odd. For these jump lengths, we show the optimal probability is \(1 - 1/q\) and construct optimal lawns. For a \textit{pair} of antipodal lawns, we show that the optimal probability of jumping from one onto the other is \(1 - 1/q\) for \(p, q\) coprime, \(p\) odd and \(q\) even, and one in all other cases. For an antipodal lawn on the sphere, it is known
[the third author and \textit{D. Pitalúa-García}, ``Bloch-sphere colorings and Bell inequalities'', Phys. Rev. A 90, Article ID 062124, 13 p. (2014; \url{doi:10.1103/PhysRevA.90.062124})]
that if \(\varphi = \pi /q\), where \(q \in \mathbb{N} \), then the optimal retention probability of \(1 - 1/q\) for the grasshopper's jump is provided by a hemispherical lawn. We show that in all other cases where \(0 < \varphi < \pi /2\), hemispherical lawns are not optimal, disproving the hemispherical colouring maximality hypotheses
[the third author and Pitalúa-García, loc. cit.].
We discuss the implications for Bell experiments and related cryptographic tests.Local energy optimality of periodic setshttps://zbmath.org/1472.820042021-11-25T18:46:10.358925Z"Coulangeon, Renaud"https://zbmath.org/authors/?q=ai:coulangeon.renaud"Schürmann, Achill"https://zbmath.org/authors/?q=ai:schurmann.achillSummary: We study the local optimality of periodic point sets in \(\mathbb{R}^n\) for energy minimization in the Gaussian core model, that is, for radial pair potential functions \(f_c(r) = e^{-cr}\) with \(c > 0\). By considering suitable parameter spaces for \(m\)-periodic sets, we can locally rigorously analyze the energy of point sets, within the family of periodic sets having the same point density. We derive a characterization of periodic point sets being \(f_c\)-critical for all \(c\) in terms of weighted spherical 2-designs contained in the set. Especially for 2-periodic sets like the family \(\mathsf{D}^+_n\) we obtain expressions for the hessian of the energy function, allowing to certify \(f_c\)-optimality in certain cases. For odd integers \(n \geq 9\) we can hereby in particular show that \(\mathsf{D}^+_n\) is locally \(f_c\)-optimal among 2-periodic sets for all sufficiently large \(c\).Complexity in phase transforming pin-jointed auxetic latticeshttps://zbmath.org/1472.820052021-11-25T18:46:10.358925Z"Hunt, G. W."https://zbmath.org/authors/?q=ai:hunt.giles-w"Dodwell, T. J."https://zbmath.org/authors/?q=ai:dodwell.timothy-jSummary: We demonstrate the complexity that can exist in the modelling of auxetic lattices. By introducing pin-jointed members and large deformations to the analysis of a re-entrant structure, we create a material which has both auxetic and non-auxetic phases. Such lattices exhibit complex equilibrium behaviour during the highly nonlinear transition between these two states. The local response is seen to switch many times between stable and unstable states, exhibiting both positive and negative stiffnesses. However, there is shown to exist an underlying \textit{emergent modulus} over the transitional phase, to describe the average axial stiffness of a system comprising a large number of cells.Erratum to: ``On a finite range decomposition of the resolvent of a fractional power of the Laplacian''https://zbmath.org/1472.820062021-11-25T18:46:10.358925Z"Mitter, P. K."https://zbmath.org/authors/?q=ai:mitter.pronob-kErratum to the author's paper [ibid. 163, No. 5, 1235--1246 (2016; Zbl 1342.82040)].Ising-like models for stacking faults in a free electron metalhttps://zbmath.org/1472.820072021-11-25T18:46:10.358925Z"Ruffino, Martina"https://zbmath.org/authors/?q=ai:ruffino.martina"Skinner, Guy C. G."https://zbmath.org/authors/?q=ai:skinner.guy-c-g"Andritsos, Eleftherios I."https://zbmath.org/authors/?q=ai:andritsos.eleftherios-i"Paxton, Anthony T."https://zbmath.org/authors/?q=ai:paxton.anthony-tSummary: We propose an extension of the axial next nearest neighbour Ising (ANNNI) model to a general number of interactions between spins. We apply this to the calculation of stacking fault energies in magnesium---particularly challenging due to the long-ranged screening of the pseudopotential by the free electron gas. We employ both density functional theory (DFT) using highest possible precision, and generalized pseudopotential theory (GPT) in the form of an analytic, long ranged, oscillating pair potential. At the level of first neighbours, the Ising model is reasonably accurate, but higher order terms are required. In fact, our ` \(AN^{}N\) NI model' is slow to converge---an inevitable feature of the free electron-like electronic structure. In consequence, the convergence and internal consistency of the \(AN^{}N\) NI model is problematic within the most precise implementation of DFT. The GPT shows the convergence and internal consistency of the DFT bandstructure approach with electron temperature, but does not lead to loss of precision. The GPT is as accurate as a full implementation of DFT but carries the additional benefit that damping of the oscillations in the \(AN^{}N\) NI model parameters are achieved without entailing error in stacking fault energies. We trace this to the logarithmic singularity of the Lindhard function.Two-curve Green's function for 2-SLE: the boundary casehttps://zbmath.org/1472.820082021-11-25T18:46:10.358925Z"Zhan, Dapeng"https://zbmath.org/authors/?q=ai:zhan.dapeng.1|zhan.dapengSummary: We prove that for \(\kappa\in (0,8)\), if \((\eta_1,\eta_2)\) is a 2-SLE\(_\kappa\) pair in a simply connected domain \(D\) with an analytic boundary point \(z_0\), then as \(r\to 0^+\), \(P[\mathrm{dist}(z_0,\eta_j)<r,j=1,2]\) converges to a positive number for some \(\alpha>0\), which is called the two-curve Green's function. The exponent \(\alpha\) equals \(\frac{12}{\kappa}-1\) or \(2(\frac{12}{\kappa}-1)\) depending on whether \(z_0\) is one of the endpoints of \(\eta_1\) or \(\eta_2\). We also find the convergence rate and the exact formula for the Green's function up to a multiplicative constant. To derive these results, we construct two-dimensional diffusion processes and use orthogonal polynomials to obtain their transition density.Erratum to: ``Static and dynamic Green's functions in peridynamics''https://zbmath.org/1472.820092021-11-25T18:46:10.358925Z"Wang, Linjuan"https://zbmath.org/authors/?q=ai:wang.linjuan"Xu, Jifeng"https://zbmath.org/authors/?q=ai:xu.jifeng"Wang, Jianxiang"https://zbmath.org/authors/?q=ai:wang.jianxiangErratum to the authors' paper [ibid. 126, No. 1, 95--125 (2017; Zbl 1366.82013)].Infinite DLR measures and volume-type phase transitions on countable Markov shiftshttps://zbmath.org/1472.820102021-11-25T18:46:10.358925Z"Beltrán, Elmer R."https://zbmath.org/authors/?q=ai:beltran.elmer-r"Bissacot, Rodrigo"https://zbmath.org/authors/?q=ai:bissacot.rodrigo"Endo, Eric O."https://zbmath.org/authors/?q=ai:endo.eric-ossamiOn the boundary layer equations with phase transition in the kinetic theory of gaseshttps://zbmath.org/1472.820112021-11-25T18:46:10.358925Z"Bernhoff, Niclas"https://zbmath.org/authors/?q=ai:bernhoff.niclas"Golse, François"https://zbmath.org/authors/?q=ai:golse.francoisIn the present paper, the authors deal with the nonlinear half-space problem for the Boltzmann equation written in terms of the relative fluctuation of distribution function about the normalized Maxwellian \(M\) \[ \left\{ \begin{array}{cc} (\xi _i+u)\partial _xf_u+\mathcal{L}f_u, & \xi \in \mathbb{R}^3,x>0, \\
f_u(0,\xi )=f_b(\xi ), & \xi _i+u>0. \end{array} \right. \] The authors prove the existence of the curve \(C\) corresponding to solutions of the equations given in some neighborhood of the point \((1, 0, 1)\) converging as \(x\rightarrow \infty\) with exponential speed uniformly in \(u\). The authors provides a self-contained construction of the solution to the Nicolaenko-Thurber generalized eigenvalue problem near \(u = 0\). Then, the authors introduce the penalization method, and formulate the problem to be solved by a fixed point argument. The linearized penalized problem is studied. Also, the authors investigate the (weakly) nonlinear penalized problem by a fixed point argument. The authors give an alternative, possibly simpler proof of one of the results discussed in [\textit{T.-P. Liu} and \textit{S.-H. Yu}, Arch. Ration. Mech. Anal. 209, No. 3, 869--997 (2013; Zbl 1290.35181)].Corrigendum to: ``Exact enumeration of Hamiltonian walks on the \(4\times 4\times 4\) cube and applications to protein folding''https://zbmath.org/1472.820122021-11-25T18:46:10.358925Z"Schram, Raoul D."https://zbmath.org/authors/?q=ai:schram.raoul-d"Schiessel, Helmut"https://zbmath.org/authors/?q=ai:schiessel.helmutFrom the text: The number of Hamiltonian walks on the \(4\times 4\times 4\) cube on pages 12 and 13 of our paper [ibid. 46, No. 48, Article ID 485001, 14 p. (2013; Zbl 1286.82015)] is wrongly stated as 27, 747, 833, 510, 015, 886. The correct number is 27, 746, 717, 207, 772, 000. We have independently verified this number with another method.Erratum to: ``The Tracy-Widom law for some sparse random matrices''https://zbmath.org/1472.820132021-11-25T18:46:10.358925Z"Sodin, Sasha"https://zbmath.org/authors/?q=ai:sodin.sashaFrom the text: The proof of the main theorem in the author's paper [ibid. 136, No. 5, 834--841 (2009; Zbl 1177.82066)], contains a serious mistake, and Lemma 5 cannot be true as stated. For example, the probability that the graph is not
connected tends to zero slower than Eq. 4 would imply.Statistics of geometric clusters in Potts model: statistical mechanics approachhttps://zbmath.org/1472.820142021-11-25T18:46:10.358925Z"Timonin, P. N."https://zbmath.org/authors/?q=ai:timonin.p-nSummary: The percolation of Potts spins with equal values in Potts model on graphs (networks) is considered. The general method for finding the Potts clusters' size distributions is developed. It allows full description of percolation transition when a giant cluster of equal-valued Potts spins appears. The method is applied to the short-ranged q-state ferromagnetic Potts model on the Bethe lattices with the arbitrary coordination number \(z\). The analytical results for the field-temperature percolation phase diagram of geometric spin clusters and their size distribution are obtained. The last appears to be proportional to that of the classical non-correlated bond percolation with the bond probability, which depends on temperature and Potts model parameters.Spectral continuity for aperiodic quantum systems: applications of a folklore theoremhttps://zbmath.org/1472.820152021-11-25T18:46:10.358925Z"Beckus, Siegfried"https://zbmath.org/authors/?q=ai:beckus.siegfried"Bellissard, Jean"https://zbmath.org/authors/?q=ai:bellissard.jean-v"De Nittis, Giuseppe"https://zbmath.org/authors/?q=ai:de-nittis.giuseppeThe authors provide a necessary and sufficient condition for a subshift to admit periodic approximations in the Hausdorff topology. Moreover, a rigorous justification for the accuracy and reliability of algorithmic methods that are used to numerically compute the spectra of certain self-adjoint operators, namely Hamiltonians associated with subshifts that admit periodic approximations, is given.Erratum to: ``Exact results for one dimensional fluids through functional integration''https://zbmath.org/1472.820162021-11-25T18:46:10.358925Z"Fantoni, Riccardo"https://zbmath.org/authors/?q=ai:fantoni.riccardoErratum to the author's paper [ibid. 163, No. 5, 1247--1267 (2016; Zbl 1342.82082)].Constitutive relations for polar continua based on statistical mechanics and spatial averaginghttps://zbmath.org/1472.820172021-11-25T18:46:10.358925Z"Svendsen, Bob"https://zbmath.org/authors/?q=ai:svendsen.bobSummary: The purpose of the current work is the formulation of macroscopic constitutive relations, and in particular continuum flux densities, for polar continua from the underlying mass point dynamics. To this end, generic microscopic continuum field and balance relations are derived from phase space transport relations for expectation values of point fields related to additive mass point quantities. Given these, microscopic energy, linear momentum and angular momentum, balance relations are obtained in the context of the split of system forces into non-conservative and conservative parts. In addition, divergence-flux relations are formulated for the conservative part of microscopic supply-rate densities. For the case of angular momentum, two such relations are obtained. One of these is force-based, and the other is torque-based. With the help of physical and material theoretic restrictions (e.g. material frame-indifference), reduced forms of the conservative flux densities are obtained. In the last part of the work, formulation of macroscopic constitutive relations from their microscopic counterparts is investigated in the context of different spatial averaging approaches. In particular, these include (weighted) volume-averaging based on a localization function, surface averaging of normal flux densities based on Cauchy flux theory and volume averaging with respect to centre of mass.Glauber dynamics for Ising model on convergent dense graph sequenceshttps://zbmath.org/1472.820182021-11-25T18:46:10.358925Z"Acharyya, Rupam"https://zbmath.org/authors/?q=ai:acharyya.rupam"Stefankovic, Daniel"https://zbmath.org/authors/?q=ai:stefankovic.danielSummary: We study the Glauber dynamics for Ising model on (sequences of) dense graphs. We view the dense graphs through the lens of graphons [\textit{L. Lovász} and \textit{B. Szegedy}, J. Comb. Theory, Ser. B 96, No. 6, 933--957 (2006; Zbl 1113.05092)]. For the ferromagnetic Ising model with inverse temperature \(\beta\) on a convergent sequence of graphs \(\{G_n\}\) with limit graphon \(W\) we show fast mixing of the Glauber dynamics if \(\beta\lambda_1(W)<1\) and slow (torpid) mixing if \(\beta\lambda_1(W)>1\) (where \(\lambda_1(W)\) is the largest eigenvalue of the graphon). We also show that in the case \(\beta\lambda_1(W)=1\) there is insufficient information to determine the mixing time (it can be either fast or slow).
For the entire collection see [Zbl 1372.68012].Corrigendum to: ``Fermi-Pasta-Ulam chains with harmonic and anharmonic long-range interactions''https://zbmath.org/1472.820192021-11-25T18:46:10.358925Z"Chendjou, Gervais Nazaire Beukam"https://zbmath.org/authors/?q=ai:chendjou.gervais-nazaire-beukam"Nguenang, Jean Pierre"https://zbmath.org/authors/?q=ai:nguenang.jean-pierre"Trombettoni, Andrea"https://zbmath.org/authors/?q=ai:trombettoni.andrea"Dauxois, Thierry"https://zbmath.org/authors/?q=ai:dauxois.thierry"Khomeriki, Ramaz"https://zbmath.org/authors/?q=ai:khomeriki.ramaz"Ruffo, Stefano"https://zbmath.org/authors/?q=ai:ruffo.stefanoCorrigendum to the authors' paper [ibid. 60, 115--127 (2018; Zbl 1470.82018)].Frequency dispersion in the fractional Langmuir approximation for the adsorption-desorption phenomenahttps://zbmath.org/1472.820202021-11-25T18:46:10.358925Z"Barbero, Giovanni"https://zbmath.org/authors/?q=ai:barbero.giovanni"Evangelista, Luiz Roberto"https://zbmath.org/authors/?q=ai:evangelista.luiz-roberto"Lenzi, Ervin K."https://zbmath.org/authors/?q=ai:kaminski-lenzi.ervinSummary: We propose that a kinetic equation of fractional order may be used to account for the frequency dispersion of the effective parameters in the framework of the Langmuir approximation for the adsorption-desorption phenomena. A frequency dependence of these parameters naturally arises in this formalism, indicating that it may play a similar role of a generalization of the Langmuir isotherm obtained from a homogeneous distribution of relaxation times. The fractional approach formalism opens the possibility to consider different relaxation regimes characterizing the interfacial behaviour of electrolytic cells, and may be a powerful tool to interpret complex impedance spectroscopy data.Phase transition for the interchange and quantum Heisenberg models on the Hamming graphhttps://zbmath.org/1472.820212021-11-25T18:46:10.358925Z"Adamczak, Radosław"https://zbmath.org/authors/?q=ai:adamczak.radoslaw"Kotowski, Michał"https://zbmath.org/authors/?q=ai:kotowski.michal"Miłoś, Piotr"https://zbmath.org/authors/?q=ai:milos.piotrSummary: We study a family of random permutation models on the Hamming graph \(H(2,n)\) (i.e., the 2-fold Cartesian product of complete graphs), containing the interchange process and the cycle-weighted interchange process with parameter \(\theta>0\). This family contains the random walk representation of the quantum Heisenberg ferromagnet. We show that in these models the cycle structure of permutations undergoes a phase transition -- when the number of transpositions defining the permutation is \(\le cn^2\), for small enough \(c>0\), all cycles are microscopic, while for more than \(\geq Cn^2\) transpositions, for large enough \(C>0\), macroscopic cycles emerge with high probability.
We provide bounds on values \(C, c\) depending on the parameter \(\theta\) of the model, in particular for the interchange process we pinpoint exactly the critical time of the phase transition. Our results imply also the existence of a phase transition in the quantum Heisenberg ferromagnet on \(H(2,n)\), namely for low enough temperatures spontaneous magnetization occurs, while it is not the case for high temperatures.
At the core of our approach is a novel application of the cyclic random walk, which might be of independent interest. By analyzing explorations of the cyclic random walk, we show that sufficiently long cycles of a random permutation are uniformly spread on the graph, which makes it possible to compare our models to the mean-field case, i.e., the interchange process on the complete graph, extending the approach used earlier by Schramm.Absence of diagonal force constants in cubic Coulomb crystalshttps://zbmath.org/1472.820222021-11-25T18:46:10.358925Z"Andrews, Bartholomew"https://zbmath.org/authors/?q=ai:andrews.bartholomew"Conduit, Gareth"https://zbmath.org/authors/?q=ai:conduit.garethSummary: The quasi-harmonic model proposes that a crystal can be modelled as atoms connected by springs. We demonstrate how this viewpoint can be misleading: a simple application of Gauss's law shows that the ion-ion potential for a cubic Coulomb system can have no diagonal harmonic contribution and so cannot necessarily be modelled by springs. We investigate the repercussions of this observation by examining three illustrative regimes: the bare ionic, density tight-binding and density nearly-free electron models. For the bare ionic model, we demonstrate the zero elements in the force constants matrix and explain this phenomenon as a natural consequence of Poisson's law. In the density tight-binding model, we confirm that the inclusion of localized electrons stabilizes all major crystal structures at harmonic order and we construct a phase diagram of preferred structures with respect to core and valence electron radii. In the density nearly-free electron model, we verify that the inclusion of delocalized electrons, in the form of a background jellium, is enough to counterbalance the diagonal force constants matrix from the ion-ion potential in all cases and we show that a first-order perturbation to the jellium does not have a destabilizing effect. We discuss our results in connection to Wigner crystals in condensed matter, Yukawa crystals in plasma physics, as well as the elemental solids.Limit law of a second class particle in TASEP with non-random initial conditionhttps://zbmath.org/1472.820232021-11-25T18:46:10.358925Z"Ferrari, P. L."https://zbmath.org/authors/?q=ai:ferrari.patrik-lino"Ghosal, P."https://zbmath.org/authors/?q=ai:ghosal.promit|ghosal.pratik|ghosal.purnata"Nejjar, P."https://zbmath.org/authors/?q=ai:nejjar.peterIn this paper a totally asymmetric simple exclusion process (TASEP) with non-random initial condition and density \(\lambda\) on \(\mathbb{Z}_-\) and \(\rho\) on \(\mathbb{Z}_+\) as one of the simplest non-reversible interacting particle systems on \(\mathbb{Z}\) lattice is considered. An initial and further particle configurations are assumed and described by the occupation variables \(\{\eta_j\}\). Particles (first-class particles) can jump (they are independent) one step to the right only if their right neighboring site is empty. The particles cannot overtake each other and a labeling to them is associated. The position of particle \(k\) at time \(t\) is denoted by \(x_k(t)\) with the right-to-left ordering. In this paper the second-class particles are considered: when a first-class particle tries to
jump on a site occupied by a second-class particle,
the jump is not suppressed and the two particles interchanges their positions. The applications of second-class particles are very often when the interacting system generates shocks as the discontinuities in the particle density.
The main result of paper is given by Theorem 1.1 which is in the form of the limiting distribution and uses two ingredients: 1) the asymptotic independence of the last passage times from two disjoint initial set of points of a last passage percolation (LPP) model; 2) a tightness-type result on the two LPP problems (by Proposition 3.2 and Corollary 3.4) that extends to general the densities of the Pimentel method.
The paper is divided into two sections where Section 2 shows the connection between TASEP and LPP and the proof of Theorem 1.1, which is mainly based on preliminary results on the control of LPP at different points.Invariant measures for spatial contact model in small dimensionshttps://zbmath.org/1472.820242021-11-25T18:46:10.358925Z"Kondratiev, Yuri"https://zbmath.org/authors/?q=ai:kondratiev.yuri-g"Kutoviy, Oleksandr"https://zbmath.org/authors/?q=ai:kutoviy.oleksandr-v"Pirogov, Sergey"https://zbmath.org/authors/?q=ai:pirogov.sergey-a"Zhizhina, Elena"https://zbmath.org/authors/?q=ai:zhizhina.elena-anatolevnaSummary: We study invariant measures of continuous contact model in small dimensional spaces \((d=1,2)\). We prove that this system has the one-parameter set of invariant measures in the critical regime provided the dispersal kernel has a heavy tail. The convergence to these invariant measures for a broad class of initial states is established.Generation of discrete structures in phase-space via charged particle trapping by an electrostatic wavehttps://zbmath.org/1472.820252021-11-25T18:46:10.358925Z"Vainchtein, Dmitri"https://zbmath.org/authors/?q=ai:vainchtein.dmitri-l"Fridman, Greg"https://zbmath.org/authors/?q=ai:fridman.greg"Artemyev, Anton"https://zbmath.org/authors/?q=ai:artemyev.anton-vSummary: The wave-particle resonant interaction plays an important role in the charged particle energization by trapping (capture) into resonance. For the systems with waves propagating through inhomogeneous plasma, the key small parameter is the ratio of the wave wavelength to a characteristic spatial scale of inhomogeneity. When that parameter is very small, the asymptotic methods are applicable for the system description, and the resultant energy distribution of trapped particle ensemble has a typical Gaussian profile around some mean value. However, for moderate values of that parameter, the energy distribution has a fine structure including several maxima, each corresponding to the discrete number of oscillations a particle makes in the trapped state. We explain this novel effect which can play important role for generation of unstable distributions of accelerated particles in many space plasma systems.Response theory and phase transitions for the thermodynamic limit of interacting identical systemshttps://zbmath.org/1472.820262021-11-25T18:46:10.358925Z"Lucarini, Valerio"https://zbmath.org/authors/?q=ai:lucarini.valerio"Pavliotis, Grigorios A."https://zbmath.org/authors/?q=ai:pavliotis.grigorios-a"Zagli, Niccolò"https://zbmath.org/authors/?q=ai:zagli.niccoloSummary: We study the response to perturbations in the thermodynamic limit of a network of coupled identical agents undergoing a stochastic evolution which, in general, describes non-equilibrium conditions. All systems are nudged towards the common centre of mass. We derive Kramers-Kronig relations and sum rules for the linear susceptibilities obtained through mean field Fokker-Planck equations and then propose corrections relevant for the macroscopic case, which incorporates in a self-consistent way the effect of the mutual interaction between the systems. Such an interaction creates a memory effect. We are able to derive conditions determining the occurrence of phase transitions specifically due to system-to-system interactions. Such phase transitions exist in the thermodynamic limit and are associated with the divergence of the linear response but are not accompanied by the divergence in the integrated autocorrelation time for a suitably defined observable. We clarify that such endogenous phase transitions are fundamentally different from other pathologies in the linear response that can be framed in the context of critical transitions. Finally, we show how our results can elucidate the properties of the Desai-Zwanzig model and of the Bonilla-Casado-Morillo model, which feature paradigmatic equilibrium and non-equilibrium phase transitions, respectively.Captive diffusions and their applications to order-preserving dynamicshttps://zbmath.org/1472.820272021-11-25T18:46:10.358925Z"Mengütürk, Levent Ali"https://zbmath.org/authors/?q=ai:menguturk.levent-ali"Mengütürk, Murat Cahit"https://zbmath.org/authors/?q=ai:menguturk.murat-cahitSummary: We propose a class of stochastic processes that we call captive diffusions, which evolve within measurable pairs of càdlàg bounded functions that admit bounded right-derivatives at points where they are continuous. In full generality, such processes allow reflection and absorption dynamics at their boundaries -- possibly in a hybrid manner over non-overlapping time periods -- and if they are martingales, continuous boundaries are necessarily monotonic. We employ multi-dimensional captive diffusions equipped with a totally ordered set of boundaries to model random processes that preserve an initially determined rank. We run numerical simulations on several examples governed by different drift and diffusion coefficients. Applications include interacting particle systems, random matrix theory, epidemic modelling and stochastic control.Two-member Markov processes toward an equilibrium from a continuum of initial stateshttps://zbmath.org/1472.820282021-11-25T18:46:10.358925Z"Mok, Jinsik"https://zbmath.org/authors/?q=ai:mok.jinsik"Lee, Hyoung-In"https://zbmath.org/authors/?q=ai:lee.hyoung-inSummary: Dynamics of two-member Markov processes is formulated based on the binomial probability. Sets of initial states are then sought such that the final state reaches an equilibrium. On the two-parameter phase plane, such initial states are found to exhibit diverse geometric configurations depending on the source probability. Those initial-state boundaries undergo phase transitions ranging over pills, stripes, circles, ellipses, lemons, and even fuzzy shapes. These results are quite helpful in understanding several physical phenomena involving photons, electrons, and atoms. For convenience of discussion, deformations of vortices are taken as an example.Local and global perspectives on diffusion maps in the analysis of molecular systemshttps://zbmath.org/1472.820292021-11-25T18:46:10.358925Z"Trstanova, Z."https://zbmath.org/authors/?q=ai:trstanova.zofia"Leimkuhler, B."https://zbmath.org/authors/?q=ai:leimkuhler.benedict-j"Lelièvre, T."https://zbmath.org/authors/?q=ai:lelievre.tonySummary: Diffusion maps approximate the generator of Langevin dynamics from simulation data. They afford a means of identifying the slowly evolving principal modes of high-dimensional molecular systems. When combined with a biasing mechanism, diffusion maps can accelerate the sampling of the stationary Boltzmann-Gibbs distribution. In this work, we contrast the local and global perspectives on diffusion maps, based on whether or not the data distribution has been fully explored. In the global setting, we use diffusion maps to identify metastable sets and to approximate the corresponding committor functions of transitions between them. We also discuss the use of diffusion maps \textit{within} the metastable sets, formalizing the locality via the concept of the quasi-stationary distribution and justifying the convergence of diffusion maps within a local equilibrium. This perspective allows us to propose an enhanced sampling algorithm. We demonstrate the practical relevance of these approaches both for simple models and for molecular dynamics problems (alanine dipeptide and deca-alanine).A neural network-based policy iteration algorithm with global \(H^2\)-superlinear convergence for stochastic games on domainshttps://zbmath.org/1472.820302021-11-25T18:46:10.358925Z"Ito, Kazufumi"https://zbmath.org/authors/?q=ai:ito.kazufumi"Reisinger, Christoph"https://zbmath.org/authors/?q=ai:reisinger.christoph"Zhang, Yufei"https://zbmath.org/authors/?q=ai:zhang.yufeiThe following Hamilton-Jacobi-Bellman-Isaacs (HJBI) nonhomogeneous Dirichlet boundary value problem is considered: $F(u): =-a^{ij}(x)\partial_{ij}u+ G(x,u,\nabla u)=0$, for a.e. $x\in \Omega$, $\tau u=g$, on $\partial\Omega$, with a nonlinear Hamiltonian, $G(x,u,\nabla u)=\max_{\alpha \in A}\min_{\beta \in B}(b^i(x,\alpha,\beta)$ $\partial_iu(x)+c(x,\alpha,\beta)u(x) -f(x,\alpha,\beta))$. The aim here is to investigate some numerical algorithms for solving this kind of problems. The second section is devoted to basics. Under some assumptions on the coefficients, the uniqueness of the strong solution in $H^2(\Omega)$ is proved. In the third section one presents the policy iteration algorithm -- Algorithm 1 -- for the Dirichlet problem, followed by the convergence analysis. Results on semi smoothness of the HJBI operator, q-superlinear convergence of Algorithm 1 and global convergence of Algorithm 1 are proved. In the fourth section the authors develop an inexact policy algorithm for the stated Dirichlet problem. The idea is to compute an approximate solution for the linear Dirichlet problem for the iteration $u^{k+1}\in H^2(\Omega)$ in Algorithm 1, by solving an optimization problem over a set of trial functions, within a given accuracy. The new inexact policy iteration algorithm for the Dirichlet problem -- Algorithm 2 -- is presented and under some special assumptions a result on global superlinear convergence is proved. In the fifth section we find an extension of the developed iteration scheme to other boundary value problems and a connection to the artificial neural network technology. One considers a HJBI oblique derivative problem
\[
F(u): =-a^{ij}(x)\partial _{ij}u+G(x,u,\nabla u)=0,\text{ for a.e. }x\in\Omega,
\]
$Bu:=\gamma^i\tau(\partial_iu)+\gamma^0$ $\tau u-g$, on $\partial\Gamma$. Under some assumptions on the coefficients, one proves that the oblique derivative problem admits a unique strong solution in $H^2(\Omega)$. For solving the oblique derivative problem one develops a neural network-based policy iteration algorithm, Algorithm 3. The global superlinear convergence of Algorithm 3 is proved. In the sixth section, there is a large discussion on applications of the developed algorithms to the stochastic Zermelo navigation problem. Some fundamental results used in the article are resumed at the end of the paper.Optimal control model of immunotherapy for autoimmune diseaseshttps://zbmath.org/1472.820312021-11-25T18:46:10.358925Z"Costa, M. Fernanda P."https://zbmath.org/authors/?q=ai:costa.m-fernanda-p"Ramos, M. P."https://zbmath.org/authors/?q=ai:ramos.m-p-machado"Ribeiro, C."https://zbmath.org/authors/?q=ai:ribeiro.cassio-b|ribeiro.conceicao|ribeiro.claudio-d|ribeiro.cristina|ribeiro.c-c-h|ribeiro.carlos-h-c|ribeiro.celso-carneiro|ribeiro.cassilda|ribeiro.carlos-f-m|ribeiro.clovis-a|ribeiro.carlos-augusto-david|ribeiro.claudia"Soares, A. J."https://zbmath.org/authors/?q=ai:soares.ana-jacintaSummary: In this work, we develop a new mathematical model to evaluate the impact of drug therapies on autoimmunity disease. We describe the immune system interactions at the cellular level, using the kinetic theory approach, by considering self-antigen presenting cells, self-reactive T cells, immunosuppressive cells, and Interleukin-2 (IL-2) cytokines. The drug therapy consists of an intake of Interleukin-2 cytokines which boosts the effect of immunosuppressive cells on the autoimmune reaction. We also derive the macroscopic model relative to the kinetic system and study the wellposedness of the Cauchy problem for the corresponding system of equations. We formulate an optimal control problem relative to the model so that the quantity of both the self-reactive T cells that are produced in the body and the Interleukin-2 cytokines that are administrated is simultaneously minimized. Moreover, we perform some numerical tests in view of investigating optimal treatment strategies and the results reveal that the optimal control approach provides good-quality approximate solutions and shows to be a valuable procedure in identifying optimal treatment strategies.Maxwell's quasi-demon as a property of an ideal gas in the equilibrium statehttps://zbmath.org/1472.820322021-11-25T18:46:10.358925Z"Semikolenov, Andrey V."https://zbmath.org/authors/?q=ai:semikolenov.andrey-vSummary: The paper shows that for the case of an ideal gas in the equilibrium state there exists a method for splitting it into portions with different temperatures without energy transfer to or from the environment and without work being done. Compared with the thought experiment known as `Maxwell's demon', in which such splitting is based on sorting specific molecules according to their energy levels, the process described does not require the energy of a specific molecule to be determined. Here the splitting is guided by the average energy of a group of molecules. The paper establishes the fact that the average energy of molecules striking the wall over a period of time is higher than the average energy of all molecules constituting the gas; this fact is what substantiates our method. This explains how a process that may result in extracting a higher temperature portion of the gas in the equilibrium state is generally possible. The paper considers one of the implementations of this process. We also show that groups of molecules may be split off from the gas, the average energy of said groups being lower than the average energy of the gas molecules in total.Stochastic scattering model of anomalous diffusion in arrays of steady vorticeshttps://zbmath.org/1472.820332021-11-25T18:46:10.358925Z"Buonocore, Salvatore"https://zbmath.org/authors/?q=ai:buonocore.salvatore"Sen, Mihir"https://zbmath.org/authors/?q=ai:sen.mihir"Semperlotti, Fabio"https://zbmath.org/authors/?q=ai:semperlotti.fabioSummary: We investigate the occurrence of anomalous transport phenomena associated with tracer particles propagating through arrays of steady vortices. The mechanism responsible for the occurrence of anomalous transport is identified in the particle dynamic, which is characterized by long collision-less trajectories (Lévy flights) interrupted by chaotic interactions with vortices. The process is studied via stochastic molecular models that are able to capture the underlying non-local nature of the transport mechanism. These models, however, are not well suited for problems where computational efficiency is an enabling factor. We show that fractional-order continuum models provide an excellent alternative that is able to capture the non-local nature of anomalous transport processes in turbulent environments. The equivalence between stochastic molecular and fractional continuum models is demonstrated both theoretically and numerically. In particular, the onset and the temporal evolution of heavy-tailed diffused fields are shown to be accurately captured, from a macroscopic perspective, by a fractional diffusion equation. The resulting anomalous transport mechanism, for the selected ranges of density of the vortices, shows a superdiffusive nature.Coherent electronic transport in periodic crystalshttps://zbmath.org/1472.820342021-11-25T18:46:10.358925Z"Cancès, Eric"https://zbmath.org/authors/?q=ai:cances.eric"Fermanian Kammerer, Clotilde"https://zbmath.org/authors/?q=ai:fermanian-kammerer.clotilde"Levitt, Antoine"https://zbmath.org/authors/?q=ai:levitt.antoine"Siraj-Dine, Sami"https://zbmath.org/authors/?q=ai:siraj-dine.samiSummary: We consider independent electrons in a periodic crystal in their ground state, and turn on a uniform electric field at some prescribed time. We rigorously define the current per unit volume and study its properties using both linear response and adiabatic theory. Our results provide a unified framework for various phenomena such as the quantization of Hall conductivity of insulators with broken time-reversibility, the ballistic regime of electrons in metals, Bloch oscillations in the long-time response of metals, and the static conductivity of graphene. We identify explicitly the regime in which each holds.Gramian solutions and soliton interactions for a generalized (3 + 1)-dimensional variable-coefficient Kadomtsev-Petviashvili equation in a plasma or fluidhttps://zbmath.org/1472.820352021-11-25T18:46:10.358925Z"Chen, Su-Su"https://zbmath.org/authors/?q=ai:chen.su-su"Tian, Bo"https://zbmath.org/authors/?q=ai:tian.boSummary: Plasmas and fluids are of current interest, supporting a variety of wave phenomena. Plasmas are believed to be possibly the most abundant form of visible matter in the Universe. Investigation in this paper is given to a generalized (3 + 1)-dimensional variable-coefficient Kadomtsev-Petviashvili equation for the nonlinear phenomena in a plasma or fluid. Based on the existing bilinear form, \(N\)-soliton solutions in the Gramian are derived, where \(N = 1, 2, 3\)\dots{}. With \(N = 3\), three-soliton solutions are constructed. Fission and fusion for the three solitons are presented. Effects of the variable coefficients, i.e. \(h(t), l(t), q(t), n(t)\) and \(m(t)\), on the soliton fission and fusion are revealed: soliton velocity is related to \(h(t), l(t), q(t), n(t)\) and \(m(t)\), while the soliton amplitude cannot be affected by them, where \(t\) is the scaled temporal coordinate, \(h(t), l(t)\) and \(q(t)\) give the perturbed effects, and \(m(t)\) and \(n(t)\), respectively, stand for the disturbed wave velocities along two transverse spatial coordinates. We show the three parallel solitons with the same direction.Contribution of 1D topological states to the extraordinary thermoelectric properties of \(Bi_2 Te_3\)https://zbmath.org/1472.820362021-11-25T18:46:10.358925Z"Chudzinski, P."https://zbmath.org/authors/?q=ai:chudzinski.pSummary: Topological insulators are frequently also one of the best-known thermoelectric materials. It has been recently discovered that in three-dimensional (3D) topological insulators each skew dislocation can host a pair of one-dimensional (1D) topological states---a helical Tomonaga-Luttinger liquid (TLL). We derive exact analytical formulae for thermoelectric Seebeck coefficient in TLL and investigate up to what extent one can ascribe the outstanding thermoelectric properties of \(Bi_2 Te_3\) to these 1D topological states. To this end we take a model of a dense dislocation network and find an analytic formula for an overlap between 1D (the TLL) and 3D electronic states. Our study is applicable to a weakly \(n\)-doped \(Bi_2 Te_3\) but also to a broader class of nano-structured materials with artificially created 1D systems. Furthermore, our results can be used at finite frequency settings, e.g. to capture transport activated by photo-excitations.On the Nernst-Planck-Navier-Stokes systemhttps://zbmath.org/1472.820372021-11-25T18:46:10.358925Z"Constantin, Peter"https://zbmath.org/authors/?q=ai:constantin.peter"Ignatova, Mihaela"https://zbmath.org/authors/?q=ai:ignatova.mihaelaIn this paper the authors study and obtain results about global existence and stability properties and convergence properties to Boltzmann states of a model for ionic electrodiffusion in fluids, in bounded domains for various boundary conditions and a wide class of initial data. For the Nernst-Planck-Navier-Stokes model the Navier-Stokes and Poisson equations are considered. This extends earlier known results for smaller classes of initial data and local existence. The model has various applications in the physics literature.Correction to: ``A rational framework for dynamic homogenization at finite wavelengths and frequencies''https://zbmath.org/1472.820382021-11-25T18:46:10.358925Z"Guzina, Bojan B."https://zbmath.org/authors/?q=ai:guzina.bojan-b"Meng, Shixu"https://zbmath.org/authors/?q=ai:meng.shixu"Oudghiri-Idrissi, Othman"https://zbmath.org/authors/?q=ai:oudghiri-idrissi.othmanCorrects several figures, equations, and references in [the authors, ibid. 475, No. 2223, Article ID 20180547, 30 p. (2019; Zbl 1427.82047)].A regularized phase-field model for faceting in a kinetically controlled crystal growthhttps://zbmath.org/1472.820392021-11-25T18:46:10.358925Z"Philippe, T."https://zbmath.org/authors/?q=ai:philippe.t"Henry, H."https://zbmath.org/authors/?q=ai:henry.herve"Plapp, M."https://zbmath.org/authors/?q=ai:plapp.mathisSummary: At equilibrium, the shape of a strongly anisotropic crystal exhibits corners when for some orientations the surface stiffness is negative. In the sharp-interface problem, the surface free energy is traditionally augmented with a curvature-dependent term in order to round the corners and regularize the dynamic equations that describe the motion of such interfaces. In this paper, we adopt a diffuse interface description and present a phase-field model for strongly anisotropic crystals that is regularized using an approximation of the Willmore energy. The Allen-Cahn equation is employed to model kinetically controlled crystal growth. Using the method of matched asymptotic expansions, it is shown that the model converges to the sharp-interface theory proposed by Herring. Then, the stress tensor is used to derive the force acting on the diffuse interface and to examine the properties of a corner at equilibrium. Finally, the coarsening dynamics of the faceting instability during growth is investigated. Phase-field simulations reveal the existence of a parabolic regime, with the mean facet length evolving in \(\sqrt{t} \), with \(t\) the time, as predicted by the sharp-interface theory. A specific coarsening mechanism is observed: a hill disappears as the two neighbouring valleys merge.Liquid crystals on deformable surfaceshttps://zbmath.org/1472.820402021-11-25T18:46:10.358925Z"Nitschke, Ingo"https://zbmath.org/authors/?q=ai:nitschke.ingo"Reuther, Sebastian"https://zbmath.org/authors/?q=ai:reuther.sebastian"Voigt, Axel"https://zbmath.org/authors/?q=ai:voigt.axelSummary: Liquid crystals with molecules constrained to the tangent bundle of a curved surface show interesting phenomena resulting from the tight coupling of the elastic and bulk-free energies of the liquid crystal with geometric properties of the surface. We derive a thermodynamically consistent Landau-de Gennes-Helfrich model which considers the simultaneous relaxation of the \(Q\)-tensor field and the surface. The resulting system of tensor-valued surface partial differential equation and geometric evolution laws is numerically solved to tackle the rich dynamics of this system and to compute the resulting equilibrium shape. The results strongly depend on the intrinsic and extrinsic curvature contributions and lead to unexpected asymmetric shapes.Correction to: ``On the computation of hybrid modes in planar layered waveguides with multiple anisotropic conductive sheets''https://zbmath.org/1472.820412021-11-25T18:46:10.358925Z"Michalski, K. A."https://zbmath.org/authors/?q=ai:michalski.krzysztof-a"Mustafa, M. M."https://zbmath.org/authors/?q=ai:mustafa.m-mCorrects a misprint in eq. 2.27 in the authors' paper [ibid. 474, No. 2218, Article ID 20180288, 20 p. (2018; Zbl 1407.82067)].Direct and converse nonlinear magnetoelectric coupling in multiferroic composites with ferromagnetic and ferroelectric phaseshttps://zbmath.org/1472.820422021-11-25T18:46:10.358925Z"Zhang, Juanjuan"https://zbmath.org/authors/?q=ai:zhang.juanjuan"Fang, Chao"https://zbmath.org/authors/?q=ai:fang.chao"Weng, George J."https://zbmath.org/authors/?q=ai:weng.george-jSummary: In this paper, we develop a theoretical principle to calculate the direct and converse magnetoelectric (ME) coupling response of ferromagnetic/ferroelectric composites with 2-2 connectivity. We first present an experimentally based constitutive equation for Terfenol-D, and then build the mechanism of domain switch for the ferroelectric phase. In the latter, the change of Gibbs free energy, thermodynamic driving force and kinetic equations for domain growth are also established. These two sets of constitutive equations are shown to capture the experimental data of Terfenol-D and PZT, respectively, well. For the direct effect under an applied magnetic field, the induced electric field and the overall ME coupling coefficient are determined. For the converse effect under an applied electric field, the induced magnetization and the excited magnetic field are obtained. Both the induced electric filed under direct effect and the excited magnetic field under converse effect are shown to display the hysteretic characteristics, and also in good agreement with experiments. We conclude that the developed theory can both qualitatively and quantitatively reflect the essential features of nonlinear direct and converse ME coupling of the multiferroic composites.Spin-flip scattering engendered quantum spin torque in a Josephson junctionhttps://zbmath.org/1472.820432021-11-25T18:46:10.358925Z"Pal, Subhajit"https://zbmath.org/authors/?q=ai:pal.subhajit"Benjamin, Colin"https://zbmath.org/authors/?q=ai:benjamin.colinSummary: We examine a Josephson junction with two ferromagnets and a magnetic impurity sandwiched between two superconductors. In such ferromagnetic Josephson junctions, equilibrium spin torque exists only when ferromagnets are misaligned. This is explained via the `conventional' mechanism of spin transfer torque, which owes its origin to the misalignment of two ferromagnets. However, we see surprisingly when the magnetic moments of the ferromagnets are aligned parallel or anti-parallel, there is a finite equilibrium spin torque due to the quantum mechanism of spin-flip scattering. We explore the properties of this unique spin-flip scattering-induced equilibrium quantum spin torque, especially its tunability via exchange coupling and phase difference across the superconductors.Mass-based finite volume scheme for aggregation, growth and nucleation population balance equationhttps://zbmath.org/1472.820442021-11-25T18:46:10.358925Z"Singh, Mehakpreet"https://zbmath.org/authors/?q=ai:singh.mehakpreet"Ismail, Hamza Y."https://zbmath.org/authors/?q=ai:ismail.hamza-y"Matsoukas, Themis"https://zbmath.org/authors/?q=ai:matsoukas.themis"Albadarin, Ahmad B."https://zbmath.org/authors/?q=ai:albadarin.ahmad-b"Walker, Gavin"https://zbmath.org/authors/?q=ai:walker.gavinSummary: In this paper, a new mass-based numerical method is developed using the notion of \textit{L. Forestier-Coste} and \textit{S. Mancini} [SIAM J. Sci. Comput. 34, No. 6, B840--B860 (2012; Zbl 1259.82054)] for solving a one-dimensional aggregation population balance equation. The existing scheme requires a large number of grids to predict both moments and number density function accurately, making it computationally very expensive. Therefore, a mass-based finite volume is developed which leads to the accurate prediction of different integral properties of number distribution functions using fewer grids. The new mass-based and existing finite volume schemes are extended to solve simultaneous aggregation-growth and aggregation-nucleation problems. To check the accuracy and efficiency, the mass-based formulation is compared with the existing method for two kinds of benchmark kernels, namely analytically solvable and practical oriented kernels. The comparison reveals that the mass-based method computes both number distribution functions and moments more accurately and efficiently than the existing method.Evolution of local motifs and topological proximity in self-assembled quasi-crystalline phaseshttps://zbmath.org/1472.820452021-11-25T18:46:10.358925Z"Pedersen, Martin Cramer"https://zbmath.org/authors/?q=ai:pedersen.martin-cramer"Robins, Vanessa"https://zbmath.org/authors/?q=ai:robins.vanessa"Mortensen, Kell"https://zbmath.org/authors/?q=ai:mortensen.kell"Kirkensgaard, Jacob J. K."https://zbmath.org/authors/?q=ai:kirkensgaard.jacob-j-kSummary: Using methods from the field of topological data analysis, we investigate the self-assembly and emergence of three-dimensional quasi-crystalline structures in a single-component colloidal system. Combining molecular dynamics and persistent homology, we analyse the time evolution of persistence diagrams and particular local structural motifs. Our analysis reveals the formation and dissipation of specific particle constellations in these trajectories, and shows that the persistence diagrams are sensitive to nucleation and convergence to a final structure. Identification of local motifs allows quantification of the similarities between the final structures in a topological sense. This analysis reveals a continuous variation with density between crystalline clathrate, quasi-crystalline, and disordered phases quantified by `topological proximity', a visualization of the Wasserstein distances between persistence diagrams. From a topological perspective, there is a subtle, but direct connection between quasi-crystalline, crystalline and disordered states. Our results demonstrate that topological data analysis provides detailed insights into molecular self-assembly.Dark matter as dark dwarfs and other macroscopic objects: multiverse relics?https://zbmath.org/1472.830442021-11-25T18:46:10.358925Z"Gross, Christian"https://zbmath.org/authors/?q=ai:gross.christian"Landini, Giacomo"https://zbmath.org/authors/?q=ai:landini.giacomo"Strumia, Alessandro"https://zbmath.org/authors/?q=ai:strumia.alessandro"Teresi, Daniele"https://zbmath.org/authors/?q=ai:teresi.danieleSummary: First order phase transitions can leave relic pockets of false vacua and their particles, that manifest as macroscopic Dark Matter. We compute one predictive model: a gauge theory with a dark quark relic heavier than the confinement scale. During the first order phase transition to confinement, dark quarks remain in the false vacuum and get compressed, forming Fermi balls that can undergo gravitational collapse to stable dark dwarfs (bound states analogous to white dwarfs) near the Chandrasekhar limit, or primordial black holes.Nonlinearly charged dyonic black holeshttps://zbmath.org/1472.830582021-11-25T18:46:10.358925Z"Panahiyan, Shahram"https://zbmath.org/authors/?q=ai:panahiyan.shahramSummary: In this paper, we investigate the thermodynamics of dyonic black holes in the presence of Born-Infeld electromagnetic field. We show that electric-magnetic duality reported for dyonic solutions with Maxwell field is omitted in case of Born-Infeld generalization. We also confirm that generalization to nonlinear field provides the possibility of canceling the effects of cosmological constant. This is done for nonlinearity parameter with \(10^{-33}\) \(\text{eV}^2\) order of magnitude which is high nonlinearity regime. In addition, we show that for small electric/magnetic charge and high nonlinearity regime, black holes would develop critical behavior and several phases. In contrast, for highly charged case and Maxwell limits (small nonlinearity), black holes have one thermal stable phase. We also find that the pressure of the cold black holes is bounded by some constraints on its volume while hot black holes' pressure has physical behavior for any volume. In addition, we report on possibility of existences of triple point and reentrant of phase transition in thermodynamics of these black holes. Finally, we show that if electric and magnetic charges are identical, the behavior of our solutions would be Maxwell like (independent of nonlinear parameter and field). In other words, nonlinearity of electromagnetic field becomes evident only when these black holes are charged magnetically and electrically different.Non-standard magnetohydrodynamics equations and their implications in sunspotshttps://zbmath.org/1472.850022021-11-25T18:46:10.358925Z"El-Nabulsi, Rami Ahmad"https://zbmath.org/authors/?q=ai:el-nabulsi.rami-ahmadSummary: In this work, we study the physics of plasma waves and magnetohydrodynamic (MHD) equilibrium of sunspots based on the concept of non-standard Lagrangians which play an important role in several branches of science. We derived the modified fluid equations from the Maxwell-Vlasov equation using the moment conventional procedure. Several new interaction terms between physical quantities arise in the non-standard MHD (NS-MHD) equations that give rise to additional features in plasma MHD. A number of fundamental problems in plasma physics are discussed including the non-relativistic dynamics of inviscid fluid subject to the gravitational field, linear waves in plasma MHD and MHD equilibrium of sunspots. For the case of magnetoacoustic wave, it was observed that the NS-MHD equations modify the dispersion relation and its corresponding velocity depends on the sign (positive or negative) of the free parameters introduced in the theory. The non-standard Alfvén velocity is greater than the standard Alfvén velocity for the negative sign and smaller for the positive sign. Besides, in the MHD equilibrium of sunspots, non-standard MHD extends the conventional problem by adding several constraints that lead to an emergence of very low temperature inside the magnetic flux tube comparable to what is observed in low-temperature superconductors. Additional consequences are discussed accordingly.