Crossover to the KPZ equation

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 $γ\in(1/2,1]$, 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.

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