Approach to asymptotically diffusive behavior for Brownian particles in media with periodic diffusivities

David S. Dean, Thomas Guérin
2014 Physical Review E  
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
more » ... ect 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.
doi:10.1103/physreve.90.062114 pmid:25615051 fatcat:sndny6vpivd3xh7qe4a4ctmpoq