Journal of Statistical Physics最新文献

We propose a new kinetic BGK-type model for a mixture of four monatomic gases, undergoing a bimolecular and reversible chemical reaction. The elastic and reactive interactions are described separately by distinct relaxation terms and the mechanical operator is the sum of binary BGK contributions, one for each pair of interacting species. In this way, our model separately incorporates the effects of mechanical processes and chemical reactions. Additionally, it retains the effects of inter-species interactions which are proper of the mixture. The dependence of Maxwellian attractors on the main macroscopic fields is explicitly expressed by assuming that the exchange rates for momentum and energy of mechanical and chemical operators coincide with the ones of the corresponding Boltzmann terms. Under suitable hypotheses, the relaxation of the distribution functions to equilibrium is shown through entropy dissipation. Some numerical simulations are included to investigate the trend to equilibrium.

In this paper, we derive distributional convergence rates for the magnetization vector and the maximum pseudolikelihood estimator of the inverse temperature parameter in the tensor Curie–Weiss Potts model. Limit theorems for the magnetization vector have been derived recently in Bhowal and Mukherjee (arXiv preprint, arXiv:2307.01052, 2023), where several phase transition phenomena in terms of the scaling of the (centered) magnetization and its asymptotic distribution were established, depending upon the position of the true parameters in the parameter space. In the current work, we establish Berry–Esseen type results for the magnetization vector, specifying its rate of convergence at these different phases. At “most” points in the parameter space, this rate is (N^{-1/2}) (N being the size of the Curie–Weiss network), while at some special points, the rate is either (N^{-1/4}) or (N^{-1/6}), depending upon the behavior of the fourth derivative of a certain negative free energy function at these special points. These results are then used to derive Berry–Esseen type bounds for the maximum pseudolikelihood estimator of the inverse temperature parameter whenever it lies above a certain criticality threshold.

The Lindblad equation, which describes Markovian quantum dynamics under dissipation, is usually derived under the weak system-bath coupling assumption. Strong system-bath coupling often leads to non-Markov evolution. The singular-coupling limit is known as an exception: it yields a Lindblad equation with an arbitrary strength of dissipation. However, the singular-coupling limit requires high-temperature limit of the bath, and hence the system ends up in a trivial infinite-temperature state, which is not desirable in the context of quantum control. In this work, it is shown that we can derive a Markovian Lindblad equation for an arbitrary strength of the system-bath coupling by considering a new scaling limit that is called the singular-driving limit, which combines the singular-coupling limit and fast periodic driving. In contrast to the standard singular-coupling limit, an interplay between dissipation and periodic driving results in a nontrivial steady state.

We address the problem of stability of one-dimensional non-periodic ground-state configurations in classical lattice-gas models with respect to finite-range perturbations of interactions. We show that a relevant property of ground-state configurations in this context is their homogeneity. The so-called strict boundary condition says that the number of finite patterns of a configuration has bounded fluctuations uniform in any finite subset of the lattice (mathbb Z). We show that if the strict boundary condition is not satisfied and interactions between particles decay at least as fast as (1/r^{alpha }) with (alpha >2), then ground-state configurations are not stable. In the Thue–Morse ground state, the number of finite patterns may fluctuate as much as the logarithm of the length of a lattice subset. We show that the Thue–Morse ground state is unstable for any (alpha >1) with respect to arbitrarily small two-body interactions favoring the presence of molecules consisting of two neighboring up or down spins. We also investigate Sturmian systems defined by irrational rotations on the circle. They satisfy the strict boundary condition but nevertheless they are unstable for (alpha >3).

We study the time evolution of an incompressible fluid with axial symmetry without swirl when the vorticity is sharply concentrated on N annuli of radii of the order of (r_0) and thickness (varepsilon ). We prove that when (r_0= |log varepsilon |^alpha ), (alpha >1), the vorticity field of the fluid converges for (varepsilon rightarrow 0) to the point vortex model, in an interval of time which diverges as (log |log varepsilon |). This generalizes previous result by Cavallaro and Marchioro in (J Math Phys 62:053102, 2021), that assumed (alpha >2) and in which the convergence was proved for short times only.

In this paper, we study a mean-field spin model with three- and two-body interactions. In a recent paper (Ann Henri Poincaré, 2024) by Contucci, Mingione and Osabutey, the equilibrium measure for large volumes was shown to have three pure states, two with opposite magnetization and an unpolarized one with zero magnetization, merging at the critical point. The authors proved a central limit theorem for the suitably rescaled magnetization. The aim of our paper is presenting a prove of a central limit theorem for the rescaled magnetization applying the exchangeable pair approach due to Stein. Moreover we prove (non-uniform) Berry–Esseen bounds, a concentration inequality, Cramér-type moderate deviations and a moderate deviations principle for the suitably rescaled magnetization. Interestingly we analyze Berry–Esseen bounds in case the model-parameters ((K_n,J_n)) converge to the critical point (0, 1) on lines with different slopes and with a certain speed, and obtain new limiting distributions and thresholds for the speed of convergence.

We consider the diluted multi-species Sherrington–Kirkpatrick (DMSK) model in which the variance of disorders depend on the species the particles belong to, and the number of edges within each block is diluted. First, we find the annealed region of the DMSK model at high temperature and compute the corresponding free energy. Next, we get a fluctuation result for the overlap vector through a differential method. Lastly, by using cavity method, we obtain the corresponding replica symmetric bound and r-step of replica symmetry breaking bound.

We study a hierarchical model of non-overlapping cubes of sidelengths (2^j), (jin {mathbb {Z}}). The model allows for cubes of arbitrarily small size and the activities need not be translationally invariant. It can also be recast as a spin system on a tree with a long-range hard-core interaction. We prove necessary and sufficient conditions for the existence and uniqueness of Gibbs measures, discuss fragmentation and condensation, and prove bounds on the decay of two-point correlation functions.

This paper is devoted to investigating Freidlin–Wentzell’s large deviation principle for one (spatial) dimensional nonlinear stochastic wave equation (frac{partial ^2 u^{{varepsilon }}(t,x)}{partial t^2}=frac{partial ^2 u^{{varepsilon }}(t,x)}{partial x^2}+sqrt{{varepsilon }}sigma (t, x, u^{{varepsilon }}(t,x))dot{W}(t,x)), where (dot{W}) is white in time and fractional in space with Hurst parameter (Hin big (frac{1}{4},frac{1}{2}big )). The variational framework and the modified weak convergence criterion proposed by Matoussi et al. (Appl Math Optim 83(2):849–879, 2021) are adopted here.

The discrete nonlinear Schrödinger equation on ({mathbb Z}^d), (d ge 1) is an example of a dispersive nonlinear wave system. Being a Hamiltonian system that conserves also the (ell ^2({mathbb Z}^d))-norm, the well-posedness of the corresponding Cauchy problem follows for square-summable initial data. In this paper, we prove that the well-posedness continues to hold for initial data that can grow towards infinity, namely anything that has at most a certain power law growth far away from the origin. The growth condition is loose enough to guarantee that, at least in dimension (d=1), initial data sampled from any reasonable equilibrium distribution of the defocusing DNLS satisfies it almost surely.