Shocks in the asymmetric exclusion process with internal degree of freedom

TL;DR

This paper characterizes Markovian three-state lattice gases with pair interactions, focusing on asymmetric exclusion processes with particles in two nonconserved states, and analyzes shock dynamics including drift and diffusion.

Contribution

It identifies conditions on transition rates that simplify shock structure and describes shock dynamics in a novel three-state exclusion process.

Findings

Derived conditions for simple shock structure

Calculated shock drift velocity

Determined shock diffusion coefficient

Abstract

We determine all families of Markovian three-states lattice gases with pair interaction and a single local conservation law. One such family of models is an asymmetric exclusion process where particles exist in two different nonconserved states. We derive conditions on the transition rates between the two states such that the shock has a particularly simple structure with minimal intrinsic shock width and random walk dynamics. We calculate the drift velocity and diffusion coefficient of the shock.