Abstract
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.
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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.
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.
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).
M. H. Ernst, J. R. Dorfman, W. R. Hoegy, and J. M. J. van Leeuwen,Physica 45:127 (1969).
H. van Beijeren and J. R. Dorfman,J. Stat. Phys. 23:335 (1980).
J. R. Dorfman and E. G. D. Cohen,Phys. Rev. A 6:776 (1972).
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Dedicated to Prof. E. G. D. Cohen on the occasion of his 65th birthday.
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Dorfman, J.R., Ernst, M.H. Hard-sphere binary-collision operators. J Stat Phys 57, 581–593 (1989). https://doi.org/10.1007/BF01022823
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DOI: https://doi.org/10.1007/BF01022823