Fixed points and boundary layers in exclusion processes

TL;DR

This paper introduces a fixed point boundary layer analysis approach to study phases and phase transitions in asymmetric simple exclusion processes, including a two-species ASEP with unique phase behavior.

Contribution

It presents a novel fixed point boundary layer method for analyzing phase transitions in ASEPs, applied to both single and two-species models.

Findings

Identified new phase transitions in two-species ASEP

Provided insights into boundary layer behavior in exclusion processes

Demonstrated the method's effectiveness on simple single-species ASEP

Abstract

In this paper, we show how a fixed point based boundary layer analysis can be used to understand phases and phase transitions in asymmetric simple exclusion processes (ASEPs) with open boundaries. In order to illustrate this method, we choose a two-species ASEP which has interesting phase transitions not seen in the one-species case. We also apply this method to the single species problem where the analysis is simple but nevertheless quite insightful.