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

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.