Bethe Ansatz calculation of the spectral gap of the asymmetric exclusion process

TL;DR

This paper derives the spectral gap of the totally asymmetric exclusion process using Bethe Ansatz, simplifying the equations to a transcendental form involving polylogarithms, and extends the method to arbitrary densities.

Contribution

A new derivation of the spectral gap for ASEP using Bethe Ansatz that simplifies the equations and applies to arbitrary particle densities.

Findings

Spectral gap expressed via a transcendental equation involving polylogarithms.

Method applicable to systems with any particle density.

Explicit calculation of the dynamical exponent.

Abstract

We present a new derivation of the spectral gap of the totally asymmetric exclusion process on a half-filled ring of size L by using the Bethe Ansatz. We show that, in the large L limit, the Bethe equations reduce to a simple transcendental equation involving the polylogarithm, a classical special function. By solving that equation, the gap and the dynamical exponent are readily obtained. Our method can be extended to a system with an arbitrary density of particles. Keywords: ASEP, Bethe Ansatz, Dynamical Exponent, Spectral Gap.