Exact Relaxation Dynamics in the Totally Asymmetric Simple Exclusion Process

TL;DR

This paper investigates the exact relaxation dynamics of the TASEP on a ring with step initial conditions, revealing unique behaviors and scaling laws through Bethe ansatz analysis.

Contribution

It provides the first exact analysis of the full relaxation process in TASEP, including finite-size scaling of local densities and currents.

Findings

Emergence of ripples in density profiles

Existence of excessive particle currents

Scaling exponents of -3/2 and -1 for amplitudes

Abstract

The relaxation dynamics of the one-dimensional totally asymmetric simple exclusion process on a ring is considered in the case of step initial condition. Analyzing the time evolution of the local particle densities and currents by the Bethe ansatz method, we examine their full relaxation dynamics. As a result, we observe peculiar behaviors, such as the emergence of a ripple in the density profile and the existence of the excessive particle currents. Moreover, by making a finite-size scaling analysis of the asymptotic amplitudes of the local densities and currents, we find the scaling exponents with respect to the total number of sites to be -3/2 and -1 respectively.