Hard-sphere binary-collision operators
The time displacement operator is described for a system of hard-sphere particles. We show how to avoid needing a representation for this operator in unphysical regions of phase space, and how to construct a useful representation in terms of binary collision operators in the physical region. The various binary collision operators used for hard-sphere systems are derived for the case of a system of two spheres, and the results are generalized toN-particle systems.
Key wordsBinary collision operator hard spheres kinetic theory Liouville operator
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- 1.E. G. D. Cohen and I. M. de Schepper, inFundamental Problems in Statistical Mechanics IV, E. G. D. Cohen and W. Fiszdon, eds. (Ossolineum, Wroclaw, 1978), p. 101.Google Scholar
- 2.T. R. Kirkpatrick and J. R. Dorfman, inMolecular Dynamics Simulations of Statistical Mechanical Systems, G. Ciccoti and W. Hoover, eds. (Plenum Press, New York, 1986), p. 260.Google Scholar
- 3.C. F. W. Götze, inProceedings of the NATO Advanced Study Institute on Amorphous and Liquid Materials, E. Lüscheu, G. Jacucci, and G. Fritsch, eds. (Reidel, Dordrecht, 1986).Google Scholar
- 4.M. H. Ernst, J. R. Dorfman, W. R. Hoegy, and J. M. J. van Leeuwen,Physica 45:127 (1969).Google Scholar
- 5.H. van Beijeren and J. R. Dorfman,J. Stat. Phys. 23:335 (1980).Google Scholar
- 6.J. R. Dorfman and E. G. D. Cohen,Phys. Rev. A 6:776 (1972).Google Scholar