Current fluctuations in a partially asymmetric simple exclusion process with a defect particle

TL;DR

This paper analyzes a partially asymmetric exclusion process with a defect particle on a ring, using Bethe ansatz to exactly compute currents and fluctuations, revealing phase-dependent behaviors and validating results with simulations.

Contribution

It introduces an integrable model with a free defect in a partially asymmetric bath and provides exact analytical results for currents and fluctuations.

Findings

Localized or shock phases depend on parameters

Exact mean currents and diffusion constants calculated

Results agree well with Monte-Carlo simulations

Abstract

We study an exclusion process on a ring comprising a free defect particle in a bath of normal particles. The model is one of the few integrable cases in which the bath particles are partially asymmetric. The presence of the free defect creates localized or shock phases according to parameter values. We use a functional approach to Bethe equations resulting from a nested Bethe ansatz to calculate exactly the mean currents and diffusion constants. The results agree very well with Monte-Carlo simulations and reveal the main modes of fluctuation in the different phases of the steady state.