title: Approach to asymptotically diffusive behavior for Brownian particles in media with periodic diffusivities.
abstract: We analyze the mean squared displacement of a Brownian particle in a medium with a spatially varying local diffusivity, which is assumed to be periodic. When the system is asymptotically diffusive, the mean-squared displacement, characterizing the dispersion in the system, is, at late times, a linear function of time. A Kubo-type formula is given for the mean-squared displacement, which allows the recovery of some known results for the effective diffusion constant D(e) in a direct way, but also allows an understanding of the asymptotic approach to the diffusive limit. In particular, as well as as computing the slope of a linear fit to the late-time mean-squared displacement, we find a formula for the constant where the fit intersects the y axis.
authors.affiliation: Université de Bordeaux and CNRS, Laboratoire Ondes et Matière d'Aquitaine (LOMA), UMR 5798, F-33400 Talence, France.
authors.forename: David S
authors.initials: DS
authors.lastname: Dean
authors.affiliation: Université de Bordeaux and CNRS, Laboratoire Ondes et Matière d'Aquitaine (LOMA), UMR 5798, F-33400 Talence, France.
authors.forename: Thomas
authors.initials: T
authors.lastname: Guérin