The Study of Shocks in Three-States Driven-Diffusive Systems: A Matrix Product Approach

TL;DR

This paper investigates shock structures in three-state driven-diffusive systems using a matrix product approach, identifying specific systems where shocks behave as random walks with calculable diffusion and drift properties.

Contribution

It characterizes three families of three-state systems with shock measures expressible as superpositions, and derives their shock dynamics parameters.

Findings

Three families of three-states systems have shock measures as superpositions.

Shocks perform random walks under certain constraints.

Diffusion coefficients and drift velocities are explicitly calculated.

Abstract

We study the shock structures in three-states one-dimensional driven-diffusive systems with nearest neighbors interactions using a matrix product formalism. We consider the cases in which the stationary probability distribution function of the system can be written in terms of superposition of product shock measures. We show that only three families of three-states systems have this property. In each case the shock performs a random walk provided that some constraints are fulfilled. We calculate the diffusion coefficient and drift velocity of shock for each family.