Asymmetric Exclusion Processes with Disorder: Effect of Correlations

TL;DR

This paper investigates how correlations affect the behavior of asymmetric exclusion processes with disorder, revealing the importance of correlations in phase transitions and particle dynamics through theoretical and simulation methods.

Contribution

It introduces approximate analytical methods and a numerical iterative procedure to analyze correlations in disordered asymmetric exclusion processes, supported by Monte Carlo simulations.

Findings

Correlations significantly influence particle dynamics.

Proximity of defect bonds shifts correlations between system regions.

Theoretical predictions align with simulation results.

Abstract

Multi-particle dynamics in one-dimensional asymmetric exclusion processes with disorder is investigated theoretically by computational and analytical methods. It is argued that the general phase diagram consists of three non-equilibrium phases that are determined by the dynamic behavior at the entrance, at the exit and at the slowest defect bond in the bulk of the system. Specifically, we consider dynamics of asymmetric exclusion process with two identical defect bonds as a function of distance between them. Two approximate theoretical methods, that treat the system as a sequence of segments with exact description of dynamics inside the segments and neglect correlations between them, are presented. In addition, a numerical iterative procedure for calculating dynamic properties of asymmetric exclusion systems is developed. Our theoretical predictions are compared with extensive Monte Carlo computer simulations. It is shown that correlations play an important role in the particle dynamics. When two defect bonds are far away from each other the strongest correlations are found at these bonds. However, bringing defect bonds closer leads to the shift of correlations to the region between them.