Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries

TL;DR

This paper investigates the spectral properties of the partially asymmetric exclusion process with open boundaries, extending previous totally asymmetric results to partial symmetry, and analyzes how the spectral gap scales with system size.

Contribution

It extends the analysis of the Bethe ansatz spectrum from totally asymmetric to partially asymmetric exclusion processes with open boundaries, including finite-size scaling of the spectral gap.

Findings

Finite-size scaling of the spectral gap determined

Boundary-induced crossovers observed

Results interpreted via effective domain wall theories

Abstract

We analyze the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process on a finite lattice and with the most general open boundary conditions. We extend results obtained recently for totally asymmetric diffusion [J. de Gier and F.H.L. Essler, J. Stat. Mech. P12011 (2006)] to the case of partial symmetry. We determine the finite-size scaling of the spectral gap, which characterizes the approach to stationarity at large times, in the low and high density regimes and on the coexistence line. We observe boundary induced crossovers and discuss possible interpretations of our results in terms of effective domain wall theories.