Approximation of the Linear Boltzmann Equation by the Fokker-Planck Equation
- 5 October 1967
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 162 (1), 186-188
- https://doi.org/10.1103/physrev.162.186
Abstract
In general, transformation of the linear Boltzmann integral operator to a differential operator leads to a differential operator of infinite order. For purposes of mathematical tractability this operator is usually truncated at a finite order and thus questions arise as to the validity of the resulting approximation. In this paper we show that the linear Boltzmann equation can be properly approximated only by the first two terms of the Kramers-Moyal expansion; i.e., the Fokker-Planck equation, with the retention of a finite number of higher-order terms leading to a logical inconsistency.Keywords
This publication has 9 references indexed in Scilit:
- Generalizations and extensions of the Fokker- Planck-Kolmogorov equationsIEEE Transactions on Information Theory, 1967
- Energy Loss to a Cold Background Gas. I. Higher Order Corrections to the Fokker-Planck Operator for a Lorentz GasPhysical Review B, 1966
- Small-parameter expansions of linear Boltzmann collision operatorsPhysica, 1965
- On the Relaxation of the Hard—Sphere Rayleigh and Lorentz GasThe Journal of Chemical Physics, 1964
- A POWER SERIES EXPANSION OF THE MASTER EQUATIONCanadian Journal of Physics, 1961
- Differential-Operator Approximations to the Linear Boltzmann EquationJournal of Mathematical Physics, 1960
- Fluctuations from the Nonequilibrium Steady StateReviews of Modern Physics, 1960
- On Brownian motion, Boltzmann’s equation, and the Fokker-Planck equationQuarterly of Applied Mathematics, 1952
- Brownian motion in a field of force and the diffusion model of chemical reactionsPhysica, 1940