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Exact Statistical Mechanics of a One-Dimensional Self-Gravitating System

Published online by Cambridge University Press:  12 April 2016

George B. Rybicki
George B. Rybicki*
Affiliation:
Smithsonian Astrophysical Observatory, Cambridge, Mass. 02138, U.S.A.

Abstract

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The statistical mechanics of an isolated self-gravitating system consisting of N uniform mass sheets is considered using both canonical and microcanonical ensembles. The one-particle distribution function is found in closed form. The limit for large numbers of sheets with fixed total mass and energy is taken and is shown to yield the isothermal solution of the Vlasov equation. The order of magnitude of the approach to Vlasov theory is found to be 0(1/N). Numerical results for spatial density and velocity distributions are given.

Type
Research Article
Information
International Astronomical Union Colloquium , Volume 10: Gravitational N-Body Problem , November 1971 , pp. 56 - 72
Copyright
Copyright © Reidel 1971

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