Generic nonequilibrium steady states in an exclusion process on an inhomogeneous ring

TL;DR

This paper studies a one-dimensional exclusion process on an inhomogeneous ring, revealing various steady state domain wall behaviors and transitions, and providing a framework for predicting density profiles in complex inhomogeneous systems.

Contribution

It introduces a comprehensive analysis of steady states in an exclusion process with multiple inhomogeneous segments, including domain wall localization and delocalization, and offers a method to construct density profiles for arbitrary segment configurations.

Findings

Identification of localized and delocalized domain walls in steady states

Construction of steady state density profiles for multiple segments

Analysis of fluctuation scaling of domain walls

Abstract

We consider a one-dimensional totally asymmetric exclusion process on a ring with extended inhomogeneities, consisting of several segments with different hopping rates. Depending upon the underlying inhomogeneity configurations and for moderate densities, our model displays both localised (LDW) and delocalised (DDW) domain walls and delocalisation transitions of LDWs in the steady states. Our results allow us to construct the possible steady state density profiles for an arbitrary number of segments with unequal hopping rates. We explore the scaling properties of the fluctuations of LDWs and DDWs.