Related papers: Integer Lattice Gases at Equilibrium
Lattice molecule models are proposed in order to study statistical mechanics of glass transition in finite dimensions. Molecules in the models are represented by hard Wang tiles and their density is controlled by a chemical potential. An…
We study the statistical mechanics of a two-dimensional gas with a repulsive delta function interaction, using a mean field approximation. By a direct counting of states we establish that this model obeys exclusion statistics and is…
We show that non-relativistic Quantum Mechanics can be faithfully represented in terms of a classical diffusion process endowed with a gauge symmetry of group Z_4. The representation is based on a quantization condition for the realized…
Molecular dynamics simulations of a three dimensional relativistic gas with a soft potential are conducted with different interactions and particle masses. For all cases the velocity distribution agrees numerically with the J\"uttner…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
Gauge-invariance is a fundamental concept in Physics -- known to provide mathematical justification for the fundamental forces. In this paper, we provide discrete counterparts to the main gauge theoretical concepts directly in terms of…
We use a Hamiltonian dynamics to discuss the statistical mechanics of long-lasting quasi-stationary states particularly relevant for long-range interacting systems. Despite the presence of an anomalous single-particle velocity distribution,…
Probabilistic cellular automata (PCA) are used to model a variety of discrete spatially extended systems undergoing parallel-updating. We propose an embedding of a number of classical nonequilibrium concepts in the PCA-world. We start from…
We review progress towards direct simulation of quantum dynamics in many-body systems, using recently developed stochastic gauge techniques. We consider master equations, canonical ensemble calculations and reversible quantum dynamics are…
In contrast to equilibrium systems, non-equilibrium steady states depend explicitly on the underlying dynamics. Using Monte Carlo simulations with Metropolis, Glauber and heat bath rates, we illustrate this expectation for an Ising lattice…
We investigate the dynamics of a Bose-Einstein condensate held in an optical lattice under the influence of a strong periodic driving potential. Studying the mean-field version of the Bose-Hubbard model reveals that the condensate becomes…
We have investigated the non-equilibrium nature of a lattice gas system consisting of a regular lattice of charged particles driven by an external electric field. For a big system, an exact solution cannot be obtained using a master…
We introduce a new class of cellular automata to model reaction-diffusion systems in a quantitatively correct way. The construction of the CA from the reaction-diffusion equation relies on a moving average procedure to implement diffusion,…
The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite…
A simple method to obtain a canonical partition function for one dimensional lattice gas model is presented. The simplification is based upon rewriting a sum over all possible configurations to a sum over numbers of clusters in the system.
We study the exact statistical mechanics of Lam\'e solitons using a transfer matrix method. This requires a knowledge of the first forbidden band of the corresponding Schr\"odinger equation with the periodic Lam\'e potential. Since the…
We review theoretical results obtained recently in the framework of statistical mechanics to study systems with long range forces. This fundamental and methodological study leads us to consider the different domains of applications in a…
A classical local cellular automaton can describe an interacting quantum field theory for fermions. We construct a simple classical automaton for a particular version of the Thirring model with imaginary coupling. This interacting fermionic…
The basic notions of statistical mechanics (microstates, multiplicities) are quite simple, but understanding how the second law arises from these ideas requires working with cumbersomely large numbers. To avoid getting bogged down in…
We present a lattice-based numerical method to describe the non equilibrium behavior of a simple fluid under non-uniform spatial conditions. The evolution equation for the one-particle phase-space distribution function is derived starting…