Unexpected Effects of Disorder on Current Fluctuations in the Symmetric Simple Exclusion Process

TL;DR

This paper investigates how disorder affects current fluctuations in the symmetric simple exclusion process, revealing unexpected asymmetric density dependence and the significant influence of energy landscapes on current variability.

Contribution

It provides the first exact expression for current fluctuations in SSEP with a defect and introduces an approximate method for disordered environments.

Findings

Second moment of current deviates from homogeneous case

Asymmetric density dependence observed around density 1/2

Energy landscape significantly impacts current fluctuations

Abstract

We explore how the disorder impacts the current fluctuations in the symmetric simple exclusion process (SSEP) within a heterogeneous environment. First, we analyze the SSEP with a defect site under the periodic boundary conditions. We derive the exact expression for the second moment of the current and observe deviations from that of the homogeneous system. Notably, the second moment of the current shows asymmetric density dependence around a density of 1/2 and surpassing that of the homogeneous system in the low-density region. Furthermore, based on the finding from the SSEP with a defect site, we present an approximate derivation of the second moment of the current in the SSEP on a quenched random energy landscape using a partial-mean-field approach. The second moment of the current is heavily influenced by the energy landscape, revealing unique effects arising from the interplay between the heterogeneous environment and the many-body system. Our findings provide valuable insights that can be applied to control current fluctuations in systems involving the interactions of many particles, such as biological transport.