Disorder and non-conservation in a driven diffusive system

TL;DR

This paper studies a disordered driven diffusive system with non-conserving sites, providing exact solutions in certain limits and revealing Griffiths singularities and stretched exponential decay in the system density.

Contribution

It introduces an exactly solvable model of a disordered asymmetric exclusion process with non-conservation, highlighting novel nonequilibrium phenomena.

Findings

Exact steady state solutions in two limits

Identification of Griffiths singularities in nonequilibrium

Stretched exponential decay of system density with exponent 2/5

Abstract

We consider a disordered asymmetric exclusion process in which randomly chosen sites do not conserve particle number. The model is motivated by features of many interacting molecular motors such as RNA polymerases. We solve the steady state exactly in the two limits of infinite and vanishing non-conserving rates. The first limit is used as an approximation to large but finite rates and allows the study of Griffiths singularities in a nonequilibrium steady state despite the absence of any transition in the pure model. The disorder is also shown to induce a stretched exponential decay of system density with stretching exponent \phi= 2/5.