Journal of Statistical Physics最新文献

In this paper we investigate the action of self-consistent transfer operators (STOs) on Birkhoff cones and give sufficient conditions for stability of their fixed points. Our approach relies on the order preservation properties of STOs that can be established via the study of their differential. We show that this approach is effective both in the weak coupling regime and in some strong coupling ones. In particular, we apply the construction to STOs arising from strongly coupled maps both deterministic and noisy. Our approach allows for explicit estimates that we use to give examples of STOs with multiple stable fixed points. Furthermore we show examples where some of these fixed points are far from the asymptotic statistical behaviour of the corresponding system of finite coupled maps

We provide a mathematically rigorous Keldysh functional integral for fermionic quantum field theories. We show convergence of a discrete-time Grassmann Gaussian integral representation in the time-continuum limit under very general hypotheses. We also prove analyticity of the effective action and explicit bounds for the truncated (connected) expectation values (gamma ^textrm{c}_{m,bar{m}}) of the non-equilibrium system. These bounds imply clustering with a summable decay in the thermodynamic limit, provided these properties hold at time zero, and provided that the determinant bound (delta _C) and decay constant (alpha _C) of the fermionic Keldysh covariance are bounded uniformly in the volume. We then give bounds for these constants and show that uniformity in the volume indeed holds for a general class of systems. Finally we show that in the setting of dissipative quantum systems, these bounds are not necessarily restricted to short times.

Let (Z_n(z,t)) denote the partition function of the q-state Potts Model on the rooted binary Cayley tree of depth n. Here, (z = textrm{e}^{-h/T}) and (t = textrm{e}^{-J/T}) with h denoting an externally applied magnetic field, T the temperature, and J a coupling constant. One can interpret z as a “magnetic field-like” variable and t as a “temperature-like” variable. Physical values (h in mathbb {R}, T > 0), and (J in mathbb {R}) correspond to (t in (0,infty )) and (z in (0,infty )). For any fixed (t_0 in (0,infty )) and fixed (n in mathbb {N}) we consider the complex zeros of (Z_n(z,t_0)) and how they accumulate on the ray ((0,infty )) of physical values for z as (n rightarrow infty ). In the ferromagnetic case ((J >0) or equivalently (t in (0,1))) these Lee-Yang zeros accumulate to at most one point on ((0,infty )) which we describe using explicit formulae. In the antiferromagnetic case ((J < 0) or equivalently (t in (1,infty ))) these Lee-Yang zeros accumulate to at most two points of ((0,infty )), which we again describe with explicit formulae. The same results hold for the unrooted Cayley tree of branching number two. These results are proved by adapting a renormalization procedure that was previously used in the case of the Ising model on the Cayley Tree by Müller-Hartmann and Zittartz (1974 and 1977), Barata and Marchetti (1997), and Barata and Goldbaum (2001). We then use methods from complex dynamics and, more specifically, the active/passive dichotomy for iteration of a marked point, along with detailed analysis of the renormalization mappings, to prove the main results.

Markovianity and local detailed balance (LDB) are widely regarded as two basic structural assumptions of stochastic thermodynamics. In this work, we use microcanonical ensemble theory to establish these properties for a small Hamiltonian system that is strongly coupled to its environment, also modeled as a Hamiltonian system, under the following assumptions: (i) the bath dynamics is much faster than both the system dynamics and the variation of the control parameters, i.e. time-scale separation (TSS); (ii) the bath is much larger than the system; (iii) the interaction between the system and the bath is short-ranged; (iv) the microscopic dynamics of the joint system has time-reversal symmetry, and (v) the coarse-grained dynamics of the joint system is Markovian. Under these assumptions, the bath remains in instantaneous microcanonical equilibrium conditioned on the system state and the control parameter. We decompose the total Hamiltonian such that the bath Hamiltonian is an adiabatic invariant under slow evolution of the system state and control parameters, which enforces the system Hamiltonian to be the Hamiltonian of mean force. The heat absorbed by the system is identified as the negative of the bath’s Boltzmann entropy change multiplied by T. Our approach provides a thermodynamically consistent and experimentally testable foundation for strong-coupling stochastic thermodynamics.

We consider the empirical neighborhood distribution of marked sparse Erdős-Rényi random graphs, obtained by decorating edges and vertices of a sparse Erdős-Rényi random graph with i.i.d. random elements taking values on Polish spaces. We prove that the empirical neighborhood distribution of this model satisfies a large deviation principle in the framework of local weak convergence. We rely on the concept of BC-entropy introduced by Delgosha and Anantharam (2019) which is inspired on the previous work by Bordenave and Caputo (2015). Our main technical contribution is an approximation result that allows one to pass from graph with marks in discrete spaces to marks in general Polish spaces. As an application of the results developed here, we prove a large deviation principle for interacting diffusions driven by gradient evolution and defined on top of sparse Erdős-Rényi random graphs. In particular, our results apply for the stochastic Kuramoto model. We obtain analogous results for the sparse uniform random graph with given number of edges.

We consider the hyperuniform model of d-dimensional integer lattice perturbed by independent random variables and we investigate the large scale asymptotic fluctuations of smoothed versions of the usual counting statistics, specifically of linear statistics associated to a smooth function with rapid decay at infinity. We highlight three distinct classes of limit, depending on the dimension d and on the tails of the perturbations. On the one hand, we establish that for dimensions larger than two, central limit theorems hold under mild assumptions on the perturbations. This confirms numerical observations from physics, suggesting that even for highly correlated hyperuniform models, large dimensions favor asymptotic normality. On the other hand, in dimension one, the limiting distribution can be Gaussian, non-Gaussian but characterized by a Poisson integral, or stable with parameter strictly between one and two. These two latter results represent rare examples of non-Gaussian limits for smooth linear statistics of hyperuniform point processes of Classes I and II.

Using molecular dynamics simulations, the ratio of ternary to binary collision densities is investigated for both a hard-sphere gas and a Lennard-Jones gas. The simulations confirm the existing theoretical models for the hard-sphere gas but reveal temperature dependence of collision density ratio in a Lennard-Jones gas. A theoretical model is developed to explain this temperature dependence.

For the elephant random walk, namely, the elephant random walk with deterministic step sizes, rates of moment convergence have been obtained by Hayashi, Oshiro and Takei [J. Stat. Mech. Theory Exp., 2023]. In this paper, we extend above results to the elephant random walk with random step sizes, namely, we obtained rates of moment convergence for the position of the walker when memory parameter (alpha in (-1, 1)).

Spectral form factor (SFF), one of the key quantity from random matrix theory, serves as an important tool to probe universality in disordered quantum systems and quantum chaos. In this work, we present exact closed-form expressions for the second- and third-order SFFs in the circular unitary ensemble (CUE), valid for all real values of the time parameter, and analyze their asymptotic behavior in different regimes. In particular, for the second-order SFF, we derive an exact closed-form expression in terms of polygamma functions. In the limit of infinite matrix size, and when the time parameter is restricted to integer values, the second-order SFF reproduces the standard result established in earlier studies. When the time parameter is of order one relative to the matrix size, we demonstrate that the second-order SFF grows logarithmically with the ensemble dimension. For the third-order SFFs, a closed-form result in a special case is obtained by exploiting the translational invariance of CUE.

In this paper, we study fluctuations and moderate deviations for a discrete energy Kac-like walk associated with a Boltzmann-type equation. We show that the fluctuations of the empirical measure around the Boltzmann-type equation converge in law to an infinite dimensional Ornstein-Uhlenbeck process, and establish the moderate deviation principle for the empirical measure.