Sample-to-sample fluctuations of transport coefficients in the totally asymmetric simple exclusion process with quenched disorder

TL;DR

This paper analyzes how quenched disorder affects transport properties in the TASEP, revealing non-self-averaging behavior and sample-to-sample fluctuations characterized by Weibull distribution, with analytical insights into maximal current and diffusion coefficient.

Contribution

It provides analytical expressions for transport coefficients in disordered TASEP and demonstrates non-self-averaging effects using extreme value theory.

Findings

Maximal current and diffusion coefficient depend on disorder and are non-self-averaging.

Sample-to-sample fluctuations follow Weibull distribution.

Disorder averages of transport coefficients vanish as system size increases.

Abstract

We consider the totally asymmetric simple exclusion processes on quenched random energy landscapes. We show that the current and the diffusion coefficient differ from those for homogeneous environments. Using the mean-field approximation, we analytically obtain the site density when the particle density is low or high. As a result, the current and the diffusion coefficient are described by the dilute limit of particles or holes, respectively. However, in the intermediate regime, due to the many-body effect, the current and the diffusion coefficient differ from those for single-particle dynamics. The current is almost constant and becomes the maximal value in the intermediate regime. Moreover, the diffusion coefficient decreases with the particle density in the intermediate regime. We obtain analytical expressions for the maximal current and the diffusion coefficient based on the renewal theory. The deepest energy depth plays a central role in determining the maximal current and the diffusion coefficient. As a result, the maximal current and the diffusion coefficient depend crucially on the disorder, i.e., non-self-averaging. Based on the extreme value theory, we find that sample-to-sample fluctuations of the maximal current and diffusion coefficient are characterized by the Weibull distribution. We show that the disorder averages of the maximal current and the diffusion coefficient converge to zero as the system size is increased and quantify the degree of the non-self-averaging effect for the maximal current and the diffusion coefficient.