%0 Journal Article
%T Overdamped limit and inverse friction expansion for the Brownian motion in an inhomogeneous medium
%A Xavier Durang
%A Chulan Kwon
%A Hyunggyu Park
%J Physics
%D 2013
%I arXiv
%R 10.1103/PhysRevE.91.062118
%X We revisit the problem of the overdamped (large friction) limit of the Brownian dynamics in an inhomogeneous medium characterized by a position-dependent friction coefficient and a multiplicative noise (local temperature) in one space dimension. Starting from the Kramers equation and analyzing it through the expansion in terms of eigenfunctions of a quantum harmonic oscillator, we derive analytically the corresponding Fokker-Planck equation in the overdamped limit. The result is fully consistent with the previous finding by Sancho, San Miguel, and D\"urr \cite{Sanc82}. Our method allows us to generalize the Brinkman's hierarchy, and thus it would be straightforward to obtain higher-order corrections in a systematic inverse friction expansion without any assumption. Our results are confirmed by numerical simulations for simple examples.
%U http://arxiv.org/abs/1309.5750v5