Multi-shocks in asymmetric simple exclusions processes: Insights from fixed-point analysis of the boundary-layers

TL;DR

This paper uses fixed-point analysis of boundary layers to understand phase transitions and shock structures in an asymmetric simple exclusion process with non-conservation and inter-particle repulsion.

Contribution

It introduces a boundary-layer fixed-point method to analyze phase behavior and shock phenomena in complex exclusion processes, providing both qualitative insights and quantitative results.

Findings

Identification of phase boundaries via fixed points

Characterization of shock structures in density profiles

Quantitative analysis of boundary-layer properties

Abstract

The boundary-induced phase transitions in an asymmetric simple exclusion process with inter-particle repulsion and bulk non-conservation are analyzed through the fixed points of the boundary layers. This system is known to have phases in which particle density profiles have different kinds of shocks. We show how this boundary-layer fixed-point method allows us to gain physical insights on the nature of the phases and also to obtain several quantitative results on the density profiles especially on the nature of the boundary-layers and shocks.