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Collision brackets in quantum kinetic theory

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  • Calkoen, Ch.J.
  • van Weert, Ch.G.

Abstract

The method for reducing collision brackets, developed in a previous paper, is applied to a hot classical plasma, a highly degenerate plasma, and a neutrino-nucleus system as a particular example of a Lorentz model. Various known results are rederived from a unified point of view, and generalized relativistically. In particular the quantum-mechanical Balescu-Guernsey-Lenard (BGL) bracket is studied and reduced to a twofold collision integral. With regards to degenerate systems, the method is shown to be superior to the standard phase-space decomposition (PSD) approximation to the extent that the first finite-temperature contribution, which may be substantial, is furnished correctly. For a statistically screened interaction this is corroborated by numerical calculation of the exact fourfold integral expression for the collision bracket, which appears to be well suited for integration by the Monte Carlo routine VEGAS.

Suggested Citation

  • Calkoen, Ch.J. & van Weert, Ch.G., 1986. "Collision brackets in quantum kinetic theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 135(2), pages 370-387.
    • Handle: RePEc:eee:phsmap:v:135:y:1986:i:2:p:370-387
    DOI: 10.1016/0378-4371(86)90149-4
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    1. Oppenfeld, Horst Von & Sta. Iglesia, Jesus C. & Librero, Florentino, 1962. "Results of a Study of Adoption of Better Farm Practices in the Philippines," Indian Journal of Agricultural Economics, Indian Society of Agricultural Economics, vol. 17(4), pages 1-11.
    2. van Erkelens, H., 1981. "Relativistic Boltzmann theory for a plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 107(1), pages 48-70.
    3. van Weert, Ch.G. & Leermakers, M.C.J. & Hooiveld, A.J.W. & Mensonides, F., 1984. "Normal modes of a relativistic quantum plasma; The one-component plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 127(3), pages 388-406.
    4. Piasecki, J. & Wajnryb, E., 1985. "The Lorentz model for neutrinos: Exact solution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 133(1), pages 291-301.
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