The Edwards–Wilkinson equation with drift and Neumann boundary conditions

Abstract

The well-known scaling of the Edwards–Wilkinson equation is essentially determined by dimensional analysis. In a range of experimental setups, be it due to the presence of an electrical or a gravitational field, or the indirect effect of other terms or an expansion, an additional drift term has to be considered. Once the drift term is added, more sophisticated reasoning is required to determine the scaling, which initially suggests that the drift term dominates the diffusion. However, the diffusion term is dangerously irrelevant and the resulting scaling in fact non-trivial. In order to assess the universality of the Edwards–Wilkinson equation with drift and to describe a physically more relevant situation, we compare the scaling obtained with Neumann boundary conditions to the published case with Dirichlet boundary conditions.