Journal of Statistical Physics最新文献

The mean-field limit of interacting particle systems with singular interaction potentials under reflecting boundary conditions in non-convex domains is considered. To rigorously connect the microscopic particle system with its mesoscopic counterpart, we construct the empirical measure and establish stability by means of weighted exponential functionals. The main technical difficulties arise from the combination of non-convex geometry and singular particle interactions. To overcome the latter, we employ a smoothing (mollification) procedure of the interaction kernel, and then pass to the singular limit. For the boundary contribution, we exploit the exact shape of the boundary to keep the reflection terms under control. By combining moment bounds, stopping-time arguments, and mean-square error estimates for the empirical measure, we prove propagation of chaos and convergence to the reflected McKean-Vlasov equation.

According to Born (Atomic Physics, page 103), spectra are “quantum phenomena, which from a classical standpoint are perfectly unintelligible”. However we illustrate results on classical calculations of infrared spectra of ionic crystals (actually LiF) which show that the situation is much more complex. Indeed it turns out that: 1) At room temperature and at higher ones (up to 1060 K) the classical computations reproduce the experimental data, even better than the presently available quantum ones do; 2) At lower temperatures (even at 7.5 K), the classical computations reproduce pretty well the data, if one accepts the idea advanced in 1916 by Nernst (the inventor of the third principle) that zero-point energy has room in classical physics too. It is eventually pointed out that the mentioned results might be regarded as a first step towards an implementation of the Einstein Classical Program, which aims at deducing quantum physics (admittedly the correct theory) from a realistic theory. In fact, we are considering the Einstein classical program in the extreme version in which the realistic theory is just (essentially, see below) classical electrodynamics of matter in bulk, involving phase space orbits, solutions of Newton equations. An Appendix is devoted to illustrate the Nernst approach, which concerns also the relation between equipartition and Planck’s law.

The eigenvalue spectrum of the sum of large random matrices that are mutually “free”, i.e., randomly rotated, can be obtained using the formalism of R-transforms, with many applications in different fields. We provide a direct interpretation of the otherwise abstract additivity property of R-transforms for the sum in terms of a dynamical evolution of “particles” (the eigenvalues), interacting through two-body and higher-body forces and subject to a Gaussian noise, generalizing the usual Dyson Brownian motion with Coulomb interaction. Interestingly, the appearance of an outlier outside of the bulk of the spectrum is signalled by a divergence of the “velocity” of the generalized Dyson motion. We also investigate the evolution of eigenvectors, extend our results to products of free matrices, and study the singular values of a non-Hermitian matrix perturbed by a bi-invariant random matrix.

In this paper, we study the large-time behaviors of the Kuramoto-Sivashinsky equation (KSE) on the 1D torus while being subjected to random perturbation via additive Gaussian noise. It is well-known that under suitable assumptions on the stochastic forcing, the KSE admits a unique invariant probability measure. In this work, we make further progress on the topic of ergodicity by addressing the issue of convergence rate toward equilibrium. In comparison with the previous results, we can prove that the unique invariant probability measure is exponentially attractive and smallness condition of anti-diffusion coefficient is not necessary here. The proof relies on a coupling argument while making use of Lyapunov functions motivated by those of deterministic equations.

We study a finite-velocity random motion on the real line with alternating velocities (-v) and c, subject to stochastic resetting to the origin. At each velocity-switching epoch, a Bernoulli trial determines whether the particle is instantaneously reset to the origin with probability (theta ) or it continues its motion with the opposite velocity with probability (1-theta ). The resulting reset times form a renewal process. We derive the probability distributions of the position-velocity process when the intertimes between consecutive velocity changes have identical (i) exponential distribution, and (ii) Erlang-2 distribution. We also obtain explicit expressions for the moments of the position process and, in case (i), the mean-square distance between the process with resetting and an independent counterpart without resetting. We further characterize the stationary distribution, expressing it in terms of the asymptotic average of the local time of the position process. Finally, we investigate the limiting behavior of the position density under a Kac-type scaling. In both cases (i) and (ii), the position density, conditioned on random initial velocity, converges to that of the Brownian motion with Poisson resetting.

In this paper, we study strong solutions and decay estimates for an incompressible Vlasov-magnetohydrodynamic (Vlasov-MHD) model arising in magnetized plasmas. This model consists of the Vlasov equation and the incompressible MHD equations, which interact mutually through the Lorentz force. It can be readily verified that the system has two equilibria: ((bar{f},bar{u},bar{B})=(0,0,0)) and (( tilde{f},tilde{u},tilde{B})=((2pi )^{- frac{3}{2}}e^{- frac{|v|^2}{2}},0,0)). For any prescribed time interval, we establish the existence and uniqueness of strong solutions under appropriately small initial perturbations that depend on the length of the interval. In both the whole-space and periodic settings, we further derive the corresponding decay estimates for the fluid velocity and magnetic field over the interval of existence. The primary difficulty stems from the lack of drag-type or Fokker–Planck dissipation in the kinetic equation, along with the trilinear coupling generated by the Lorentz force. To address this issue, we combine the characteristic method, support propagation for the kinetic component, refined energy estimates, and Fourier analysis.

We investigate the Glauber dynamics of the generalized (2+1)-dimensional p-SOS model((1<p<infty )) under a hard floor constraint. This setting induces entropic repulsion: the integer-valued interface height is forced to remain above the wall and consequently rises to a typical height H(p, L) that depends on both the parameter p and the lattice size L. The phenomenon of entropic repulsion has been extensively studied in a variety of random interface models. In the classical SOS model ((p=1)), [8, 9] derived an exponential lower bound for the mixing time, demonstrating that the Glauber dynamics mixes only after an exponentially long time in the low-temperature regime (large (beta ), the inverse temperature). However, beyond this case, no rigorous lower bounds were previously known: even for the widely studied Discrete Gaussian model ((p=2)), the metastable slowdown predicted by the entropic repulsion picture had remained an open problem. On the equilibrium side, [18] obtained sharp large-deviation principles and precise estimates of typical and maximal heights for all (1le p<infty ), but the dynamical consequences of these results had not been established. Our main contribution is to close this gap by proving that exponentially slow(stretched-exponential) mixing arising from entropic repulsion persists throughout the regime (1<p<infty ). Specifically, we establish an exponential lower bound, showing that the mixing time satisfies (tau _{textrm{mix}}ge exp {left( cL^{1-o(1)}right) }) for some (c>0) depending on p and (beta ). In addition, we provide a refined metastability analysis, proving that the hitting time of an intermediate level aH(p, L) is at least (exp {left( cL^{a^{d(p)}-o(1)}right) }), where (0<a<1) and d(p) is a positive function depending on p. The proof relies on an extension of the classical Peierls-type contour estimates, originally developed for (p=1), to the nonlinear p-SOS setting. Taken together, these results demonstrate that entropic repulsion induces uniformly slow mixing across the entire p-SOS family, thereby extending a phenomenon that had previously been established only for (p=1).

This study focuses on establishing the large deviation principle (LDP) for a complex-valued fractional Ginzburg-Landau equation (GLE) influenced by nonlinear noise over the unbounded domain (mathbb {R}^d). Initially, we prove the well-posedness of the related deterministic control system and obtain the uniform tail estimates for its solutions. Subsequently, we show that the set of controlled solutions exhibits strong convergence when the controls are equipped with the weak topology. By examining the distributional convergence of stochastic solutions as (varepsilon rightarrow 0), we rigorously derive the LDP using the weak convergence method. A key challenge arises from the absence of compact Sobolev embeddings in unbounded domains. To address this, uniform tail estimates are introduced, which ensure the tightness of the induced probability measures and the precompactness of control paths. Additionally, the nonlinear drift term ((mu + inu )|X|^{p-2}X) is handled under the admissible constraint (|(p-2)nu | le 2mu sqrt{p-1}), guaranteeing uniqueness, continuity, and convergence of solutions. The validity of the results is preserved under the replacement of ((-Delta )^alpha ) by the classical Laplace operator. Lastly, numerical experiments are conducted to demonstrate the impact of noise intensity on solution behavior and to provide computational confirmation of the LDP.

The emergence of diffusion is one of the deepest physical phenomena observed in many-body interacting, chaotic systems. But establishing rigorously that correlation functions, say of the spin, expand diffusively, remains one of the most important problems of mathematical physics. We establish for the first time, with Lindbladian evolution, a lower bound on spin diffusion in chaotic, translation-invariant, nearest-neighbor open quantum spin-1/2 chain satisfying a local unitality condition and strong conservation of magnetization. The bound is strictly positive if and only if the local quantum jumps transport spin. Physically, the bound comes from the spreading effects of initial-state macroscopic fluctuations, a mechanism which occurs whenever spin is an interacting ballistic mode. Chaoticity means that the Hilbert space of extensive charges is spanned by magnetization; we expect this to be generic. Our main tool is the Green-Kubo formula, the mathematical technique of projection over quadratically extensive charges, and appropriate correlation decay bounds recently established. Because Lindbladian dynamics is not reversible, the Green-Kubo spin diffusion strength includes a contribution due to irreversibility, which we interpret as encoding the hydrodynamic entropy production that may occur in the forgotten environment. This, we show, vanishes for certain choices of interaction parameters, for which the Lindbladian dynamics becomes reversible. Our methods can be extended to finite or short ranges, higher spins, and other non-Hamiltonian systems such as quantum circuits. As we argue, according to the theory of nonlinear fluctuating hydrodynamics, we further expect these systems to display superdiffusion, and thus have infinite diffusivity; however this appears to still be beyond the reach of mathematical rigor.

We construct a unitarily invariant Hermitian matrix ensemble whose fixed-time eigenvalue law coincides with the Karlin–McGregor law for non-intersecting Brownian bridges with arbitrary finite multiplicities at both endpoints. This provides an explicit matrix-ensemble realization of the known mixed-type multiple orthogonal polynomial and Riemann–Hilbert description of the general multi-start/multi-end problem. We then derive several exact finite-n consequences of this construction. These include a path-space lift as an orbital Hermitian Brownian bridge and a reduction of the partition function to a single compact HCIZ integral with explicit t-dependence. We also compare the one-sided reduction with the Gaussian external-field ensemble, showing that, although the two ensembles are spectrally equivalent, their angular statistics are different. Finally, we derive fixed-time Schwinger–Dyson identities and associated resolvent relations for the dressed ensemble.