title: Overdamped limit and inverse-friction expansion for Brownian motion in an inhomogeneous medium.
abstract: 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-dimensional space. 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 Dürr [J. Stat. Phys. 28, 291 (1982)]. 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.
authors.affiliation: School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea.
authors.forename: Xavier
authors.initials: X
authors.lastname: Durang
authors.affiliation: Department of Physics, Myongji University, Yongin, Gyeonggi-Do 449-728, Korea.
authors.forename: Chulan
authors.initials: C
authors.lastname: Kwon
authors.affiliation: School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea.
authors.forename: Hyunggyu
authors.initials: H
authors.lastname: Park