Partially Asymmetric Exclusion Processes with Sitewise Disorder

TL;DR

This paper investigates the stationary and dynamic behaviors of a one-dimensional exclusion process with site-dependent disorder, revealing how barriers influence current, phase separation, and coarsening phenomena.

Contribution

It introduces a detailed analysis of the partially asymmetric exclusion process with sitewise disorder, connecting current scaling to Sinai walk exponents and describing phase separation in stationary states.

Findings

Current scales as L^{-z/2} with system size L

Stationary states exhibit phase separation with large barriers

Non-stationary processes like coarsening are analyzed

Abstract

We study the stationary properties as well as the non-stationary dynamics of the one-dimensional partially asymmetric exclusion process with position dependent random hop rates. In a finite system of $L$ sites the stationary current, $J$, is determined by the largest barrier and the corresponding waiting time, $\tau \sim J^{-1}$, is related to the waiting time of a single random walker, $\tau_{rw}$, as $\tau \sim \tau_{rw}^{1/2}$. The current is found to vanish as: $J \sim L^{-z/2}$, where $z$ is the dynamical exponent of the biased single particle Sinai walk. Typical stationary states are phase separated: At the largest barrier almost all particles queue at one side and almost all holes are at the other side. The high-density (low-density) region, is divided into $\sim L^{1/2}$ connected parts of particles (holes) which are separated by islands of holes (particles) located at the subleading barriers (valleys). We also study non-stationary processes of the system, like coarsening and invasion. Finally we discuss some related models, where particles of larger size or multiple occupation of lattice sites is considered.