Riemann surface crossover for the spectral gaps of open TASEP

TL;DR

This paper derives exact spectral gap expressions for open TASEP near maximal current phase using Riemann surface analysis, revealing a crossover between periodic and open boundary conditions.

Contribution

It introduces a novel Riemann surface framework generated by Lambert functions to analyze spectral gaps in open TASEP.

Findings

Exact spectral gap formulas for large systems

Identification of Riemann surface crossover behavior

Connection between open and periodic TASEP spectral properties

Abstract

We consider the totally asymmetric simple exclusion process with open boundaries, at the edge of the maximal current phase. Using analytic continuations from the known stationary eigenvalue, we obtain exact expressions for the spectral gaps in the limit of large system size. The underlying Riemann surface,generated by modified Lambert functions, interpolates between the one for periodic TASEP and the one for open TASEP in the maximal current phase.