Infinite reflections of shock fronts in driven diffusive systems with two species

TL;DR

This paper investigates how shock fronts in driven diffusive systems with two species reflect infinitely many times from boundaries, contrasting with single-species models where only one reflection occurs before reaching stationarity.

Contribution

It introduces reflection maps to describe boundary interactions and demonstrates the infinite reflection phenomenon in two-species driven systems.

Findings

Shock fronts reflect infinitely many times before stationarity.

Contrast with one-species models where only one reflection occurs.

Introduction of reflection maps for boundary interaction analysis.

Abstract

Interaction of a domain wall with boundaries of a system is studied for a class of stochastic driven particle models. Reflection maps are introduced for the description of this process. We show that, generically, a domain wall reflects infinitely many times from the boundaries before a stationary state can be reached. This is in an evident contrast with one-species models where the stationary density is attained after just one reflection.