Global Density Profile for Asymmetric Simple Exclusion Process from Renormalization Group Flows

TL;DR

This paper develops a renormalization group method to analyze the global density profile in the asymmetric simple exclusion process with boundary-induced phase transitions, providing analytical insights validated by numerical solutions.

Contribution

It introduces a novel RG approach using boundary layer parameters to derive the global density profile in a nonequilibrium system.

Findings

Analytical form for the global density profile derived

Scaling form matches numerical solutions

Method cures divergences in perturbative solutions

Abstract

The totally asymmetric simple exclusion process along with particle adsorption and evaporation kinetics is a model of boundary-induced nonequilibrium phase transition. In the continuum limit, the average particle density across the system is described by a singular differential equation involving multiple scales which lead to the formation of boundary layers (BL) or shocks. A renormalization group analysis is developed here by using the location and the width of the BL as the renormalization parameters. It not only allows us to cure the large distance divergences in the perturbative solution for the BL but also generates, from the BL solution, an analytical form for the global density profile. The predicted scaling form is checked against numerical solutions for finite systems.