Journal of Statistical Physics最新文献

The dissipative spectral form factor (DSFF), recently introduced in Li et al. (Phys Rev Lett 127(17):170602, 2021) for the Ginibre ensemble, is a key tool to study universal properties of dissipative quantum systems. In this work we compute the DSFF for a large class of random matrices with real or complex entries up to an intermediate time scale, confirming the predictions from Li et al. (Phys Rev Lett 127(17):170602, 2021). The analytic formula for the DSFF in the real case was previously unknown. Furthermore, we show that for short times the connected component of the DSFF exhibits a non-universal correction depending on the fourth cumulant of the entries. These results are based on the central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices Cipolloni et al. (Electron J Prob 26:1–61, 2021) and Cipolloni et al. (Commun Pure Appl Math 76(5): 946–1034, 2023).

This paper deals with the problem of finding the Fokker Planck Equation (FPE) for the single-time probability density function (PDF) that optimally approximates the single-time PDF of a 1-D Stochastic Differential Equation (SDE) with Gaussian correlated noise. In this context, we tackle two main tasks. First, we consider the case of weak noise and in this framework we give a formal ground to the effective correction, introduced elsewhere (Bianucci and Mannella in J Phys Commun 4(10):105019, 2020, https://doi.org/10.1088/2399-6528/abc54e), to the Best Fokker Planck Equation (a standard “Born-Oppenheimer” result), also covering the more general cases of multiplicative SDE. Second, we consider the FPE obtained by using the Local Linearization Approach (LLA), and we show that a generalized cumulant approach allows an understanding of why the LLA FPE performs so well, even for noises with long (but finite) time scales and large intensities.

Abstract

We study the radius of gyration (R_T) of a self-repellent fractional Brownian motion (left{ B^H_tright} _{0le tle T}) taking values in (mathbb {R}^d) . Our sharpest result is for (d=1) , where we find that with high probability, $$begin{aligned} R_T asymp T^nu , quad text {with }quad nu =frac{2}{3}left( 1+Hright) . end{aligned}$$ For (d>1) , we provide upper and lower bounds for the exponent (nu ) , but these bounds do not match.

Macroscopic equations arising out of stochastic particle systems in detailed balance (called dissipative systems or gradient flows) have a natural variational structure, which can be derived from the large-deviation rate functional for the density of the particle system. While large deviations can be studied in considerable generality, these variational structures are often restricted to systems in detailed balance. Using insights from macroscopic fluctuation theory, in this work we aim to generalise this variational connection beyond dissipative systems by augmenting densities with fluxes, which encode non-dissipative effects. Our main contribution is an abstract theory, which for a given flux-density cost and a quasipotential, provides a decomposition into dissipative and non-dissipative components and a generalised orthogonality relation between them. We then apply this abstract theory to various stochastic particle systems—independent copies of jump processes, zero-range processes, chemical-reaction networks in complex balance and lattice-gas models—without assuming detailed balance. For macroscopic equations arising out of these particle systems, we derive new variational formulations that generalise the classical gradient-flow formulation.

In traffic flow, flyovers play a vital role in reducing traffic congestion, advancing commute timing, and helping to prevent collision scenarios. Inspired by the real-life applications of flyover, we model a coupled two-lane transport system where the lanes are divided into three segments in which the particle lane switching mechanism executes only in the middle segment of the lane, and particle inclusion and expulsion kinetics are performed in first and last segment of the lane to embody the infrastructure of flyover. The nature of the system characteristics is analyzed for diverse values of particle inclusion, expulsion, and coupling rates through graphical diagrams of phase planes, density profiles, shock dynamics, and phase transitions. The time-invariant behavior of the system is inspected numerically by utilizing the well-known method of mean-field theory, and it is discovered that the biased dynamics of particle inclusion, expulsion, and fully asymmetric coupling condition yield the phase diagram to disclose more unanticipated mixed stationary phases. Besides, the system experiences the fruitful novel incident of the double shock phase when the possibility of particle inclusion occurs relatively higher than the expulsion event. Also, it is noticed that the system experiences the fascinating phenomenon of shock propagation by traveling in either vertical/horizontal direction in the shock region of the phase diagram under the symmetric coupling circumstance, such as the position of the shock suddenly transits from the right to left segment without crossing the middle segment. The calculated numerical results are in good agreement with Monte Carlo simulation.

We develop a novel cluster expansion for finite-spin lattice systems subject to multi-body quantum —and, in particular, classical— interactions. Our approach is based on the use of “decoupling parameters”, advocated by Park (J. Stat. Phys. 27, 553–576 (1982)), which relates partition functions with successive additional interaction terms. Our treatment, however, leads to an explicit expansion in a (beta )-dependent effective fugacity that permits an explicit evaluation of free energy and correlation functions at small (beta ). To determine its convergence region we adopt a relatively recent cluster summation scheme that replaces the traditional use of Kikwood-Salzburg-like integral equations by more precise sums in terms of particular tree-diagrams Bissacot et al. (J. Stat. Phys. 139, 598–617 (2010)). As an application we show that our lower bound of the radius of (beta )-analyticity is larger than Park’s for quantum systems two-body interactions.

This paper is concerned with the stochastic reaction-diffusion lattice systems defined on the entire set with both locally Lipschitz nonlinear drift and diffusion terms. The central limit theorem is derived for such infinite-dimensional stochastic systems. Moreover, the moderate deviation principle of solution processes is also established by the weak convergence method based on the variational representation of positive functionals of Brownian motion. The method relies on proving the convergence of the solutions of the controlled stochastic lattice systems.

We study the long time behaviour of a Brownian particle evolving in a dynamic random environment. Recently, Cannizzaro et al. (Ann Probab 50(6):2475–2498, 2022) proved sharp (sqrt{log })-super diffusive bounds for a Brownian particle in the curl of (a regularisation of) the 2-D Gaussian Free Field (GFF) (underline{omega }). We consider a one parameter family of Markovian and Gaussian dynamic environments which are reversible with respect to the law of (underline{omega }). Adapting their method, we show that if (sge 1), with (s=1) corresponding to the standard stochastic heat equation, then the particle stays (sqrt{log })-super diffusive, whereas if (s<1), corresponding to a fractional heat equation, then the particle becomes diffusive. In fact, for (s<1), we show that this is a particular case of Komorowski and Olla (J Funct Anal 197(1):179–211, 2003), which yields an invariance principle through a Sector Condition result. Our main results agree with the Alder–Wainwright scaling argument (see Alder and Wainwright in Phys Rev Lett 18:988–990, 1967; Alder and Wainwright in Phys Rev A 1:18–21, 1970; Alder et al. in Phys Rev A 4:233–237, 1971; Forster et al. in Phys Rev A 16:732–749, 1977) used originally in Tóth and Valkó (J Stat Phys 147(1):113–131, 2012) to predict the (log )-corrections to diffusivity. We also provide examples which display (log ^a)-super diffusive behaviour for (ain (0,1/2]).

Abstract

It is rigorously shown that an appropriate quantum annealing for any finite-dimensional spin system has no quantum first-order transition in transverse magnetization. This result can be applied to finite-dimensional spin-glass systems, where the ground state search problem is known to be hard to solve. Consequently, it is strongly suggested that the quantum first-order transition in transverse magnetization is not fatal to the difficulty of combinatorial optimization problems in quantum annealing.

We present a method to compute transport coefficients in molecular dynamics. Transport coefficients quantify the linear dependencies of fluxes in non-equilibrium systems subject to small external forcings. Whereas standard non-equilibrium approaches fix the forcing and measure the average flux induced in the system driven out of equilibrium, a dual philosophy consists in fixing the value of the flux, and measuring the average magnitude of the forcing needed to induce it. A deterministic version of this approach, named Norton dynamics, was studied in the 1980s by Evans and Morriss. In this work, we introduce a stochastic version of this method, first developing a general formal theory for a broad class of diffusion processes, and then specializing it to underdamped Langevin dynamics, which are commonly used for molecular dynamics simulations. We provide numerical evidence that the stochastic Norton method provides an equivalent measure of the linear response, and in fact demonstrate that this equivalence extends well beyond the linear response regime. This work raises many intriguing questions, both from the theoretical and the numerical perspectives.