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

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.