Slow relaxation and aging kinetics for the driven lattice gas

TL;DR

This paper uses Monte Carlo simulations to study slow relaxation and aging in driven lattice gases across different dimensions, revealing dimension-dependent behaviors and validating aging scaling laws.

Contribution

It provides a detailed numerical analysis of relaxation dynamics and aging phenomena in driven lattice gases, comparing results with existing analytic theories across multiple dimensions.

Findings

In 1D, correlations cause extremely slow relaxation to power-law decay.

In 3D, correlations are weak, and mean-field theory is sufficient.

Aging scaling behavior follows expected power laws in all studied dimensions.

Abstract

We numerically investigate the long-time behavior of the density-density auto-correlation function in driven lattice gases with particle exclusion and periodic boundary conditions in one, two, and three dimensions using precise Monte Carlo simulations. In the one-dimensional asymmetric exclusion process on a ring with half the lattice sites occupied, we find that correlations induce extremely slow relaxation to the asymptotic power law decay. We compare the crossover functions obtained from our simulations with various analytic results in the literature, and analyze the characteristic oscillations that occur in finite systems away from half-filling. As expected, in three dimensions correlations are weak and consequently the mean-field description is adequate. We also investigate the relaxation towards the nonequilibrium steady state in the two-time density-density auto-correlations, starting from strongly correlated initial conditions. We obtain simple aging scaling behavior in one, two, and three dimensions, with the expected power laws.