Universal scaling for second class particles in a one-dimensional misanthrope process

TL;DR

This paper investigates the behavior of second class particles in a generalized one-dimensional exclusion process, revealing a universal power-law decay in their distance distribution and confirming the universality of the dynamical scaling function.

Contribution

It introduces a mapping of the KLS model to a misanthrope process and demonstrates the universal scaling behavior of second class particles across this family of models.

Findings

Distance distribution decays as power -3/2 for large distances

Universal dynamical scaling function observed within the model family

Results agree with previous analytical findings for TASEP

Abstract

We consider the one-dimensional Katz-Lebowitz-Spohn (KLS) model, which is a two-parameter generalization of the Totally Asymmetric Simple Exclusion Process (TASEP) with nearest neighbour interaction. Using a powerful mapping, the KLS model can be translated into a misanthrope process. In this model, for the repulsive case, it is possible to introduce second class particles, the number of which is conserved. We study the distance distribution of second class particles in this model numerically and find that for large distances it decreases with a power -3/2. This agrees with a previous analytical result for the TASEP where the same asymptotic behaviour was found [Derrida et al. 1993]. We also study the dynamical scaling function of the distance distribution and find that it is universal within this family of models.