Shock formation in an exclusion process with creation and annihilation

TL;DR

This paper studies shock formation in an asymmetric exclusion process with particle creation and annihilation, deriving phase diagrams and analyzing shock fluctuations through mean-field equations and simulations.

Contribution

It provides an analytical approach to phase diagram derivation and shock fluctuation analysis in a non-conservative exclusion process.

Findings

Mean-field equations accurately predict phase diagrams

Shock position fluctuations follow a random walk behavior

Finite-size scaling of shock width explained

Abstract

We investigate shock formation in an asymmetric exclusion process with creation and annihilation of particles in the bulk. We show how the continuum mean-field equations can be studied analytically and hence derive the phase diagrams of the model. In the large system-size limit direct simulations of the model show that the stationary state is correctly described by the mean-field equations, thus the predicted mean field phase diagrams are expected to be exact. The emergence of shocks and the structure of the phase diagram are discussed. We also analyse the fluctuations of the shock position by using a phenomenological random walk picture of the shock dynamics. The stationary distribution of shock positions is calculated, by virtue of which the numerically determined finite-size scaling behaviour of the shock width is explained.