Dynamics of an exclusion process with creation and annihilation

TL;DR

This paper investigates the dynamical behavior of an exclusion process with particle creation and annihilation, revealing finite length and time scales in the maximum current phase and analyzing shock localization under various rate conditions.

Contribution

It introduces a phenomenological domain-wall theory to analyze the process, providing new insights into phase transitions and shock localization in systems with creation and annihilation.

Findings

Finite length and time scales in maximum current phase for finite creation and annihilation rates.

Determination of critical exponents for the transition to TASEP.

Shock localization possible even when rates scale as 1/N^a with 1<a<2.

Abstract

We examine the dynamical properties of an exclusion process with creation and annihilation of particles in the framework of a phenomenological domain-wall theory, by scaling arguments and by numerical simulation. We find that the length- and time scale are finite in the maximum current phase for finite creation- and annihilation rates as opposed to the algebraically decaying correlations of the totally asymmetric simple exclusion process (TASEP). Critical exponents of the transition to the TASEP are determined. The case where bulk creation- and annihilation rates vanish faster than the inverse of the system size N is also analyzed. We point out that shock localization is possible even for rates proportional to 1/N^a, 1<a<2.