On the higher order corrections to the Fokker-Planck equation
A. V. Plyukhin
TL;DR
This paper revisits the Rayleigh model of nonlinear Brownian motion, deriving higher-order corrections to the Fokker-Planck equation and exploring the non-Gaussian nature of the random force.
Contribution
It provides sixth-order corrections to the Fokker-Planck equation using the van Kampen expansion, enhancing previous models of nonlinear Brownian motion.
Findings
Derived higher-order corrections up to sixth order in m/M.
Clarified the origin of non-Gaussian statistics in the Langevin force.
Improved understanding of nonlinear effects in Brownian motion.
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.
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