Dynamic instability transitions in 1D driven diffusive flow with nonlocal hopping

TL;DR

This paper investigates phase transitions in a one-dimensional driven stochastic flow with nonlocal hopping, revealing how clustering influences the transition order and scaling properties.

Contribution

It introduces a detailed analysis of the instability transition in a nonlocal asymmetric exclusion process, highlighting the role of clustering and the transition's order depending on control regimes.

Findings

Second order transition when entry reservoir controls current

First order transition when bulk controls current

Linear vanishing of road density at criticality

Abstract

One-dimensional directed driven stochastic flow with competing nonlocal and local hopping events has an instability threshold from a populated phase into an empty-road (ER) phase. We implement this in the context of the asymmetric exclusion process. The nonlocal skids promote strong clustering in the stationary populated phase. Such clusters drive the dynamic phase transition and determine its scaling properties. We numerically establish that the instability transition into the ER phase is second order in the regime where the entry point reservoir controls the current and first order in the regime where the bulk is in control. The first order transition originates from a turn-about of the cluster drift velocity. At the critical line, the current remains analytic, the road density vanishes linearly, and fluctuations scale as uncorrelated noise. A self-consistent cluster dynamics analysis explains why these scaling properties remain that simple.