Brownian Motion in an N-scale periodic Potential

A. B. Duncan, G. A. Pavliotis

Published 2016-05-19Version 1

We study the problem of Brownian motion in a multiscale potential. The potential is assumed to have N+1 scales (i.e. N small scales) and to depend periodically in all the small scales. We show that for non separable potentials, i.e. potentials in which the microscale and macroscale are fully coupled, the homogenized equation is an overdamped Langevin equation with multiplicative noise driven by the free energy, for which the detailed balance condition still holds. The calculation of the effective diffusion tensor requires the solution of a system of N coupled Poisson problems.