The approach to hard-sphere brownian motion: Variational eigenfunctions and evaluation of the Rayleigh-Fokker-Planck equation

M.R. Hoare and C.H. Kaplinsky

Physica A: Statistical Mechanics and its Applications, 1975, vol. 81, issue 3, 349-368

Abstract: We present detailed tabulations of the first few eigenfunctions of the hard-sphere energy scattering kernel for a test-particle in a background heat-bath. Calculations, for a range of heat bath/test particle mass-ratios between 18 and 11024, were carried out by a Rayleigh-Ritz method using the exact solutions of the hard-sphere Fokker-Planck equation as a basis set and supplement our previously-published results for the eigenvalues alone. The results, given as expansion coefficients in this representation thus also serve to verify the accuracy of the Fokker-Planck equation itself, the departure from this equation being reflected in the off-diagonal contributions in the Rayleigh-Ritz expansion eigenvectors.

Date: 1975
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:81:y:1975:i:3:p:349-368

DOI: 10.1016/0378-4371(75)90053-9

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