Exclusion Processes with Avalanches

TL;DR

This paper studies an exclusion process with avalanches, analyzing steady states, correlation functions, and dynamic behaviors like shocks and diffusion in both symmetric and asymmetric variants.

Contribution

It introduces a well-defined avalanche-based exclusion process and derives exact results for steady states, correlations, currents, and particle diffusion.

Findings

Exact steady state correlation functions derived

Steady state current computed for asymmetric case

Diffusion coefficient determined for symmetric case

Abstract

In an exclusion process with avalanches, when a particle hops to a neighboring empty site which is adjacent to an island the particle on the other end of the island immediately hops and if it joins another island this triggers another hop. There are no restrictions on the length of islands and the duration of the avalanche. This process is well-defined in the low-density region, \rho<1/2. We describe the nature of steady states (on a ring) and determine all correlation functions. For the asymmetric version of the process, we compute the steady state current, and we describe shock and rarefaction waves which arise in the evolution of the step-function initial profile. For the symmetric version, we determine the diffusion coefficient and examine the evolution of a tagged particle.