Journal of Statistical Physics最新文献

We study Hartree–Fock theory at half-filling for the 3D anisotropic Hubbard model on a cubic lattice with hopping parameter t in the x- and y-directions and a possibly different hopping parameter (t_z) in the z-direction; this model interpolates between the 2D and 3D Hubbard models corresponding to the limiting cases (t_z=0) and (t_z=t), respectively. We first derive all-order asymptotic expansions for the density of states. Using these expansions and units such that (t=1), we analyze how the Néel temperature and the antiferromagnetic mean field depend on the coupling parameter, U, and on the hopping parameter (t_z). We derive asymptotic formulas valid in the weak coupling regime, and we study in particular the transition from the three-dimensional to the two-dimensional model as (t_z rightarrow 0). It is found that the asymptotic formulas are qualitatively different for (t_z = 0) (the two-dimensional case) and (t_z > 0) (the case of nonzero hopping in the z-direction). Our results show that certain universality features of the three-dimensional Hubbard model are lost in the limit (t_z rightarrow 0) in which the three-dimensional model reduces to the two-dimensional model.

Focusing on a famous class of interacting diffusion processes called Ginzburg–Landau dynamics, we extend the Macroscopic Fluctuations Theory to these systems in the case where the interactions are long-range, and consequently, the macroscopic effective equations are described by non-linear fractional diffusion equations.

We study non-equilibrium properties of a chain of N oscillators with both long-ranged harmonic interactions and long-range conservative noise that exchange momenta of particle pairs. We derive exact expressions for the (deterministic) energy-current auto-correlation at equilibrium, based on the kinetic approximation of the normal mode dynamics. In all cases the decay is algebraic in the thermodynamic limit. We distinguish four distinct regimes of correlation decay depending on the exponents controlling the range of deterministic and stochastic interactions. Surprisingly, we find that long-range noise breaks down the long-range correlations characteristic of low dimensional models, suggesting a normal regime in which heat transport becomes diffusive. For finite systems, we do also derive exact expressions for the finite-size corrections to the algebraic decay of the correlation. In certain regimes, these corrections are considerably large, rendering hard the estimation of transport properties from numerical data for the finite chains. Our results are tested against numerical simulations, performed with an efficient algorithm.

We study a polynuclear growth model in which the crystallites are aligned squares, as observed in micrographs of epitaxial thin films. The expected volumes of lower layers are calculated by series expansion methods. The coefficients are calculated exactly up to the 4th power in the intensity of the nucleation process or the 12th power in the time. The method is based on exact integral expressions recently obtained by the author. The resulting instantaneous growth rate or surface speed has an initial oscillation, consistent with long-standing experimental observations. The method is also applied to 1-dimensional rod crystallites and d-dimensional cubic crystallites. For large (d) the ultimate ({text{(time}} to infty )) growth rate and oscillating growth profile are obtained. The coefficients in the series are derived from basis functions, which involve only 1-dimensional spatial integrals, and which are common to all dimensions. For the second layer, the series is derived by a cluster expansion method, analogous to methods in equilibrium statistical mechanics. For higher layers, the integrands are broken down into products of pairs of nested crystallites.

We study the long-time behavior of solutions to a kinetic equation inspired by a model of sexual populations structured in phenotypes. The model features a nonlinear integral reproduction operator derived from the Fisher infinitesimal operator and a trait-dependent selection term. The reproduction operator describes here the inheritance of the mean parental traits to the offspring without variability. We show that, under assumptions on the growth of the selection rate, Dirac masses are stable around phenotypes for which the difference between the selection rate and its minimum value is less than (frac{1}{2}). Moreover, we prove the convergence in some Fourier-based distance of the centered and rescaled solution to a stationary profile under some conditions on the initial moments of the solution.

The main focus of this article is the study of ergodicity of Interacting Particle Systems (IPS). We present a simple lemma showing that scaling time is equivalent to taking the convex combination of the transition matrix of the IPS with the identity. As a consequence, the ergodic properties of IPS are invariant under this transformation. Surprisingly, this simple observation has non-trivial implications: It allows to extend any result that does not respect this invariance, which we demonstrate with examples. Additionally, we develop a recursive method to deduce decay of correlations for IPS with alphabets of arbitrary (finite) size, and apply the Time-Scaling Lemma to that as well. As an application of this new criterion we show that certain one-dimensional IPS are ergodic answering an open question of Toom et al.

Investigating an optimized efficiency of an engine is crucial for minimizing wastage. The simple two level heat engine was introduced to calculate the efficiency at maximum power.In this paper, we explore the optimum efficiency of a simple two-level heat engine that consists of two distinct energy levels coupled with two thermal baths with distinct temperatures. By employing unified energy converter criteria, we determine the optimized efficiency under two optimum operations scenario, situated between the maximum and minimum efficiency values. The minimum efficiency is associated with either zero efficiency or efficiency at maximum power. We further express the optimum efficiency in terms of scaled parameters such as power-wise, period-wise and efficiency-wise as a function of Carnot efficiency. Finally, a figure of merit is introduced to evaluate overall engine performance, reveals that the second optimization criterion exhibits better performance compared to the first criterion with the entire range of Carnot efficiency.

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.