Facilitated Asymmetric Exclusion

TL;DR

This paper studies facilitated asymmetric exclusion processes where particles move based on neighbor occupation, analyzing steady states and wave phenomena, revealing unexpected discontinuities in rarefaction waves.

Contribution

It introduces a new class of facilitated exclusion processes and characterizes their steady state currents, cluster distributions, and wave behaviors, including rarefaction wave discontinuities.

Findings

Steady state current and cluster size distribution are derived.

Downsteps develop into rarefaction waves with possible discontinuities.

Upsteps lead to shock wave formation.

Abstract

We introduce a class of facilitated asymmetric exclusion processes in which particles are pushed by neighbors from behind. For the simplest version in which a particle can hop to its vacant right neighbor only if its left neighbor is occupied, we determine the steady state current and the distribution of cluster sizes on a ring. We show that an initial density downstep develops into a rarefaction wave that can have a jump discontinuity at the leading edge, while an upstep results in a shock wave. This unexpected rarefaction wave discontinuity occurs generally for facilitated exclusion processes.