Relaxation time in a non-conserving driven-diffusive system with parallel dynamics

TL;DR

This paper introduces a one-dimensional non-conserving driven-diffusive system with parallel dynamics, analyzing its steady-state, shock dynamics, and relaxation times using matrix product and shock measure approaches.

Contribution

It presents a novel model with parallel update rules and derives its steady-state and shock dynamics analytically, expanding understanding of non-conserving driven systems.

Findings

Steady-state expressed via matrix product approach.

Shock position dynamics characterized as a random walk.

Relaxation times analyzed in the large-system-size limit.

Abstract

We introduce a two-state non-conserving driven-diffusive system in one-dimension under a discrete-time updating scheme. We show that the steady-state of the system can be obtained using a matrix product approach. On the other hand, the steady-state of the system can be expressed in terms of a linear superposition Bernoulli shock measures with random walk dynamics. The dynamics of a shock position is studied in detail. The spectrum of the transfer matrix and the relaxation times to the steady-state have also been studied in the large-system-size limit.