Disordered asymmetric simple exclusion process: mean-field treatment

TL;DR

This paper explores how disorder affects the asymmetric simple exclusion process using mean-field and continuum approaches, revealing new steady-state regimes, phase diagram shifts, and localization phenomena.

Contribution

It introduces a generalized mean-field steady state mapping for disordered ASEP and applies a Cole--Hopf transformation to interpret disorder as localization.

Findings

Disorder creates a new flat regime in the current-density plot.

Disorder shifts the high current phase boundary in open systems.

Localization length is inversely related to the disorder-induced flat section width.

Abstract

We provide two complementary approaches to the treatment of disorder in a fundamental nonequilibrium model, the asymmetric simple exclusion process. Firstly, a mean-field steady state mapping is generalized to the disordered case, where it provides a mapping of probability distributions and demonstrates how disorder results in a new flat regime in the steady state current--density plot for periodic boundary conditions. This effect was earlier observed by Tripathy and Barma but we provide treatment for more general distributions of disorder, including both numerical results and analytic expressions for the width $2\Delta_C$ of the flat section. We then apply an argument based on moving shock fronts to show how this leads to an increase in the high current region of the phase diagram for open boundary conditions. Secondly, we show how equivalent results can be obtained easily by taking the continuum limit of the problem and then using a disordered version of the well-known Cole--Hopf mapping to linearize the equation. Within this approach we show that adding disorder induces a localization transformation (verified by numerical scaling), and $\Delta_C$ maps to an inverse localization length, helping to give a new physical interpretation to the problem.