Spectrum of the totally asymmetric simple exclusion process on a periodic lattice - bulk eigenvalues

TL;DR

This paper analyzes the spectral properties of the TASEP on a periodic lattice using Bethe ansatz, deriving formulas for eigenvalues and the spectrum's edge, revealing a specific eigenvalue density behavior.

Contribution

It introduces parametric formulas for eigenvalues and characterizes the spectrum's edge and density in the thermodynamic limit for TASEP.

Findings

Eigenvalues are expressed parametrically in the thermodynamic limit.

The spectrum edge is characterized in the complex plane.

Eigenvalue density vanishes with an exponent 2/5 near zero.

Abstract

We consider the totally asymmetric simple exclusion process (TASEP) on a periodic one-dimensional lattice of L sites. Using Bethe ansatz, we derive parametric formulas for the eigenvalues of its generator in the thermodynamic limit. This allows to study the curve delimiting the edge of the spectrum in the complex plane. A functional integration over the eigenstates leads to an expression for the density of eigenvalues in the bulk of the spectrum. The density vanishes with an exponent 2/5 close to the eigenvalue 0.