Driven Lattice Gases with Quenched Disorder: Exact Results and Different Macroscopic Regimes

TL;DR

This paper provides exact solutions for the steady states of driven disordered particle systems, revealing three distinct macroscopic regimes and offering insights into their physical behaviors.

Contribution

It derives exact steady-state measures for disordered drop-push and exclusion processes in any dimension, identifying three regimes in 1D systems.

Findings

Three regimes: Vanishing-Current, Homogeneous, Segregated-Density.

Exact steady-state measures for disordered models.

Different macroscopic behaviors depending on disorder and current.

Abstract

We study the effect of quenched spatial disorder on the steady states of driven systems of interacting particles. Two sorts of models are studied: disordered drop-push processes and their generalizations, and the disordered asymmetric simple exclusion process. We write down the exact steady-state measure, and consequently a number of physical quantities explicitly, for the drop-push dynamics in any dimensions for arbitrary disorder. We find that three qualitatively different regimes of behaviour are possible in 1-$d$ disordered driven systems. In the Vanishing-Current regime, the steady-state current approaches zero in the thermodynamic limit. A system with a non-zero current can either be in the Homogeneous regime, chracterized by a single macroscopic density, or the Segregated-Density regime, with macroscopic regions of different densities. We comment on certain important constraints to be taken care of in any field theory of disordered systems.