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  • Title: Overdamped limit and inverse-friction expansion for Brownian motion in an inhomogeneous medium.
    Author: Durang X, Kwon C, Park H.
    Journal: Phys Rev E Stat Nonlin Soft Matter Phys; 2015 Jun; 91(6):062118. PubMed ID: 26172672.
    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.
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