Single-Bottleneck Approximation for Driven Lattice Gases with Disorder and Open Boundary Conditions

TL;DR

This paper introduces the single-bottleneck approximation (SBA) to analyze how disorder affects driven lattice gases with open boundaries, providing a simplified yet accurate way to predict current behavior in disordered non-equilibrium systems.

Contribution

The paper proposes the SBA as a novel method to approximate current in disordered driven lattice gases, extending its applicability to complex models like kinesin transport.

Findings

SBA accurately predicts the current in disordered systems.

Longest defect stretch dominates the current behavior.

SBA applies to models with internal states, like kinesin transport.

Abstract

We investigate the effects of disorder on driven lattice gases with open boundaries using the totally asymmetric simple exclusion process as a paradigmatic example. Disorder is realized by randomly distributed defect sites with reduced hopping rate. In contrast to equilibrium, even macroscopic quantities in disordered non-equilibrium systems depend sensitively on the defect sample. We study the current as function of the entry and exit rates and the realization of disorder and find that it is, in leading order, determined by the longest stretch of consecutive defect sites (single-bottleneck approximation, SBA). Using results from extreme value statistics the SBA allows to study ensembles with fixed defect density which gives accurate results, e.g. for the expectation value of the current. Corrections to SBA come from effective interactions of bottlenecks close to the longest one. Defects close to the boundaries can be described by effective boundary rates and lead to shifts of the phase transitions. Finally it is shown that the SBA also works for more complex models. As an example we discuss a model with internal states that has been proposed to describe transport of the kinesin KIF1A.