Crossover to the KPZ equation

• Autor(es): Gonçalves, Patrícia ; Jara, Milton
• Data: 2012
• Identificador Persistente: http://hdl.handle.net/1822/16880
• Origem: RepositóriUM - Universidade do Minho
• Assunto(s): KPZ equation; Weakly asymmetric exclusion
• Tipo de Documento: Artigo
• Idioma: Inglês

Descrição

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 $an^{2-\gamma}$ ($a,\gamma>0$) and it occurs at $\gamma=1/2$. We show that the density field is a solution of an Ornstein-Uhlenbeck equation if $\gamma\in(1/2,1]$, while for $\gamma=1/2$ it is an energy solution of the KPZ equation. The corresponding crossover for the current of particles is readily obtained.