On the higher order corrections to the Fokker-Planck equation
arXiv:cond-mat/0501676 · doi:10.1016/j.physa.2004.11.068
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 via instantaneous collisions. Using the van Kampen method of expansion of the master equation, non-linear corrections to the Fokker-Planck equation are obtained up to sixth order in the small parameter 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.
to appear in Physica A