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

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  • Hoare, M.R.
  • Kaplinsky, C.H.

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.

Suggested Citation

  • Hoare, M.R. & Kaplinsky, C.H., 1975. "The approach to hard-sphere brownian motion: Variational eigenfunctions and evaluation of the Rayleigh-Fokker-Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 81(3), pages 349-368.
    • Handle: RePEc:eee:phsmap:v:81:y:1975:i:3:p:349-368
    DOI: 10.1016/0378-4371(75)90053-9
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    Cited by:

    1. Ferrari, Leonardo, 1982. "On the velocity relaxation of a Rayleigh gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 115(1), pages 232-246.

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