Asymmetric exclusion model with impurities

TL;DR

This paper introduces an integrable asymmetric exclusion process with impurities, expanding the spectrum of known models and revealing a different scaling exponent, which could impact understanding of non-equilibrium statistical mechanics.

Contribution

It formulates a new integrable model with impurities, derives Bethe equations, and calculates the spectral gap, showing a different universality class from the standard exclusion process.

Findings

Model displays the full spectrum of the stochastic asymmetric XXZ chain.

Spectral gap calculated for totally asymmetric diffusion at half filling.

Scaling exponent identified as 5/2, differing from the KPZ class.

Abstract

An integrable asymmetric exclusion process with impurities is formulated. The model displays the full spectrum of the stochastic asymmetric XXZ chain plus new levels. We derive the Bethe equations and calculate the spectral gap for the totally asymmetric diffusion at half filling. While the standard asymmetric exclusion process without impurities belongs to the KPZ universality class with a exponent 3/2, our model has a scaling exponent 5/2.