Spectral gap of the totally asymmetric exclusion process at arbitrary filling

TL;DR

This paper derives a simple, self-contained formula for the spectral gap of the TASEP on a ring at any particle density, extending previous results limited to half-filling, by reformulating Bethe equations as a one-body problem.

Contribution

It introduces a novel, simplified approach to calculate the spectral gap of TASEP for arbitrary filling, broadening the understanding of its spectral properties.

Findings

Spectral gap formula valid for any filling fraction

Extension of previous half-filling results

Connection to large deviation functions

Abstract

We calculate the spectral gap of the Markov matrix of the totally asymmetric simple exclusion process (TASEP) on a ring of L sites with N particles. Our derivation is simple and self-contained and extends a previous calculation that was valid only for half-filling. We use a special property of the Bethe equations for TASEP to reformulate them as a one-body problem. Our method is closely related to the one used to derive exact large deviation functions of the TASEP.