Asymmetric Exclusion Process with Global Hopping

TL;DR

This paper investigates a one-dimensional asymmetric exclusion process with a special site allowing particles to hop to any empty site, revealing a non-equilibrium phase transition characterized by a shock wave formation at a critical density.

Contribution

It introduces a novel variant of the exclusion process with global hopping from a special site and analyzes its non-trivial stationary states and phase transition behavior.

Findings

Density profile exhibits a phase transition at a critical density.

Shock wave formation occurs in the bulk beyond the critical density.

System attains a non-trivial stationary state with spatially varying density.

Abstract

We study a one-dimensional totally asymmetric simple exclusion process with one special site from which particles fly to any empty site (not just to the neighboring site). The system attains a non-trivial stationary state with density profile varying over the spatial extent of the system. The density profile undergoes a non-equilibrium phase transition when the average density passes through the critical value 1-1/[4(1-ln 2)]=0.185277..., viz. in addition to the discontinuity in the vicinity of the special site, a shock wave is formed in the bulk of the system when the density exceeds the critical density.