Crossover to the KPZ Equation

Abstract

We characterize the crossover regime to the KPZ equation for a class of one-dimensional weakly asymmetric exclusion processes. The crossover depends on the strength asymmetry an 2-γ(a, γ > 0) and it occurs at γ =1/2. We show that the density field is a solution of an Ornstein-Uhlenbeck equation if γ ∈ (1/2, 1], while for γ = 1/2 it is an energy solution of the KPZ equation. The corresponding crossover for the current of particles is readily obtained. © 2011 Springer Basel AG.