Long time asymptotics of the totally asymmetric simple exclusion process

TL;DR

This paper investigates the long-term behavior of the TASEP on a ring, revealing how different initial conditions influence relaxation times and amplitudes, with implications for understanding non-equilibrium statistical mechanics.

Contribution

It provides a detailed analysis of the asymptotic relaxation dynamics of TASEP using algebraic Bethe ansatz, highlighting the role of initial conditions and eigenvalues.

Findings

Relaxation times are governed by different eigenvalues for step and alternating initial conditions.

The scaling exponent of the leading asymptotic amplitudes is -1.

Asymptotics of correlation functions like emptiness formation probability are characterized.

Abstract

We study the long time asymptotics of the relaxation dynamics of the totally asymmetric simple exclusion process on a ring. Evaluating the asymptotic amplitudes of the local currents by the algebraic Bethe ansatz method, we find the relaxation times starting from the step and alternating initial conditions are governed by different eigenvalues of the Markov matrix. In both cases, the scaling exponents of the leading asymptotic amplitudes with respect to the total number of sites are found to be -1. We also study the asymptotics of correlation functions such as the emptiness formation probability.