Asymmetric simple exclusion process in one-dimensional chains with long-range links

TL;DR

This paper investigates how adding long-range links to a one-dimensional asymmetric exclusion process alters its phase behavior, revealing new phases and phase transitions through numerical and analytical methods.

Contribution

It introduces a model with long-range shortcuts in ASEP, demonstrating the emergence of new phases and phase transitions not present in the standard chain.

Findings

Discovery of three distinct phases: empty, jammed, and shock.

Identification of a localized shock phase with phase separation.

Analytic explanation of shock formation and phase transition mechanisms.

Abstract

We study the boundary-driven asymmetric simple exclusion process (ASEP) in a one-dimensional chain with long-range links. Shortcuts are added to a chain by connecting $pL$ different pairs of sites selected randomly where $L$ and $p$ denote the chain length and the shortcut density, respectively. Particles flow into a chain at one boundary at rate $\alpha$ and out of a chain at the other boundary at rate $\beta$, while they hop inside a chain via nearest-neighbor bonds and long-range shortcuts. Without shortcuts, the model reduces to the boundary-driven ASEP in a one-dimensional chain which displays the low density, high density, and maximal current phases. Shortcuts lead to a drastic change. Numerical simulation studies suggest that there emerge three phases; an empty phase with $ \rho = 0 $, a jammed phase with $ \rho = 1 $, and a shock phase with $ 0<\rho<1$ where $\rho$ is the mean particle density. The shock phase is characterized with a phase separation between an empty region and a jammed region with a localized shock between them. The mechanism for the shock formation and the non-equilibrium phase transition is explained by an analytic theory based on a mean-field approximation and an annealed approximation.