Defect-induced phase transition in the asymmetric simple exclusion process

TL;DR

This paper investigates the critical defect hopping rate in the one-dimensional TASEP with a slow bond, providing numerical evidence that supports the mean-field prediction of a critical rate at 1, contrary to previous numerical estimates.

Contribution

The study refines numerical methods to demonstrate that the critical defect rate is actually at 1, confirming mean-field theory and recent theoretical predictions.

Findings

Critical rate r_c is greater than 0.99.

Numerical evidence supports r_c=1 as predicted by mean-field theory.

The defect has only local effects for r ≥ r_c.

Abstract

We reconsider the long-standing question of the critical defect hopping rate $r_c$ in the one-dimensional totally asymmetric exclusion process (TASEP) with a slow bond (defect). For $r< r_c$ a phase separated state is observed due to queuing at the defect site whereas for $r\geq r_c$ the defect site has only local effects on the stationary state of the homogeneous system. Mean-field theory predicts $r_c=1$ (when hopping rates outside the defect bond are equal to 1) but numerical investigations seem to indicate $r_c \approx 0.80(2)$. Here we improve the numerics to show that $r_c > 0.99$ and give strong evidence that indeed $r_c=1$ as predicted by mean-field theory, and anticipated by recent theoretical findings.