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Derivation of a Fokker–Planck equation for generalized Langevin dynamics

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  • Khan, Sharon
  • Reynolds, Andy M.

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.

Suggested Citation

  • Khan, Sharon & Reynolds, Andy M., 2005. "Derivation of a Fokker–Planck equation for generalized Langevin dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 183-188.
    • Handle: RePEc:eee:phsmap:v:350:y:2005:i:2:p:183-188
    DOI: 10.1016/j.physa.2004.11.067
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    References listed on IDEAS

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    1. Metzler, Ralf & Klafter, Joseph, 2000. "Boundary value problems for fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 107-125.
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