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On the higher order corrections to the Fokker–Planck equation

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  • Plyukhin, A.V.

Abstract

The Rayleigh model of nonlinear Brownian motion is revisited in which the heavy particle of mass M interacts with ideal gas molecules of mass m⪡M via instantaneous collisions. Using the van Kampen method of expansion of the master equation, nonlinear corrections to the Fokker–Planck equation are obtained up to sixth order in the small parameter λ=m/M, improving earlier results. The role and origin of non-Gaussian statistics of the random force in the corresponding Langevin equation are also discussed.

Suggested Citation

  • Plyukhin, A.V., 2005. "On the higher order corrections to the Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(2), pages 198-210.
    • Handle: RePEc:eee:phsmap:v:351:y:2005:i:2:p:198-210
    DOI: 10.1016/j.physa.2004.11.068
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