Derivation of a Fokker–Planck equation for generalized Langevin dynamics

Sharon Khan and Andy M. Reynolds

Physica A: Statistical Mechanics and its Applications, 2005, vol. 350, issue 2, 183-188

Abstract: A Fokker–Planck equation describing the statistical properties of Brownian particles acted upon by long-range stochastic forces with power-law correlations is derived. In contrast with previous approaches (Wang, Phys. Rev. A 45 (1992) 2), it is shown that the distribution of Brownian particles after release from a point source is broader than Gaussian and described by a Fox function. Transport is shown to be ballistic at short times and either sub-diffusive or super-diffusive at large times. The imposition of occasional trapping events onto the Brownian dynamics can result in confined diffusion (d/dt〈x2〉→0) at long times when the mean trapping time is divergent. It is suggested that such dynamics describe protein motions in cell membranes.

Keywords: Brownian; Langevin; Fokker–Planck; Fractional calculus (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:350:y:2005:i:2:p:183-188

DOI: 10.1016/j.physa.2004.11.067

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