Asymmetric exclusion model with several kinds of impurities

TL;DR

This paper introduces a new integrable asymmetric exclusion process with multiple impurity types and hierarchical dynamics, revealing novel spectral properties and scaling exponents that extend the KPZ universality class.

Contribution

It proposes a novel integrable model with multiple impurities and hierarchical dynamics, extending the spectrum and scaling behavior of the simple asymmetric exclusion process.

Findings

The model displays a full spectrum including new levels.

The first excited state shows unusual scaling exponents.

Numerical solutions support the conjectured scaling exponents.

Abstract

We formulate a new integrable asymmetric exclusion process with $N-1=0,1,2,...$ kinds of impurities and with hierarchically ordered dynamics. The model we proposed displays the full spectrum of the simple asymmetric exclusion model plus new levels. The first excited state belongs to these new levels and displays unusual scaling exponents. We conjecture that, while the simple asymmetric exclusion process without impurities belongs to the KPZ universality class with dynamical exponent 3/2, our model has a scaling exponent $3/2+N-1$. In order to check the conjecture, we solve numerically the Bethe equation with N=3 and N=4 for the totally asymmetric diffusion and found the dynamical exponents 7/2 and 9/2 in these cases.