Mean field treatment of exclusion processes with random-force disorder

TL;DR

This paper applies mean field theory to analyze the asymmetric simple exclusion process with random-force disorder, providing insights into stationary current behavior and coarsening phenomena, supported by numerical validation.

Contribution

It introduces a mean field approach to study exclusion processes with disorder and develops a phenomenological model for coarsening, aligning with numerical results.

Findings

Stationary current analysis matches earlier assumptions

Phenomenological model describes coarsening quantitatively

Numerical results validate the mean field predictions

Abstract

The asymmetric simple exclusion process with random-force disorder is studied within the mean field approximation. The stationary current through a domain with reversed bias is analyzed and the results are found to be in accordance with earlier intuitive assumptions. On the grounds of these results, a phenomenological random barrier model is applied in order to describe quantitatively the coarsening phenomena. Predictions of the theory are compared with numerical results obtained by integrating the mean field evolution equations.