Non-self-averaging of current in a totally asymmetric simple exclusion process with quenched disorder

TL;DR

This paper studies how the maximum current in a TASEP with quenched disorder varies across different disorder realizations, revealing non-self-averaging behavior and differences from single-particle dynamics.

Contribution

It provides a detailed analysis of the non-self-averaging nature of the maximum current in TASEP with quenched disorder, including theoretical derivations and fluctuation analysis.

Findings

Maximum current depends on disorder realization

Sample-to-sample fluctuations exceed those in low/high-density regimes

Disorder average of maximum current decreases with system size

Abstract

We investigate the current properties in the totally asymmetric simple exclusion process (TASEP) on a quenched random energy landscape. In low- and high-density regimes, the properties are characterized by single-particle dynamics. In the intermediate one, the current becomes constant and is maximized. Based on the renewal theory, we derive accurate results for the maximum current. The maximum current significantly depends on a disorder realization, i.e., non-self-averaging (SA). We demonstrate that the disorder average of the maximum current decreases with the system size, and the sample-to-sample fluctuations of the maximum current exceed those of current in the low- and high-density regimes. We find a significant difference between single-particle dynamics and the TASEP. In particular, the non-SA behavior of the maximum current is always observed, whereas the transition from non-SA to SA for current in single-particle dynamics exists.