Abstract
A kinetic equation is derived for the two-time phase space correlation function in a dilute classical electron gas in equilibrium. The derivation is based on a density expansion of the correlation function and the resummation of the most divergent terms in each order in the density. It is formally analogous to the ring summation used in the kinetic theory of neutral fluids. The kinetic equation obtained is consistent to first order in the plasma parameter and is the generalization of the linearized Balescu-Guersey-Lenard operator to describe spatially inhomogeneous equilibrium fluctuations. The importance of consistently treating static correlations when deriving a kinetic equation for an electron gas is stressed. A systematic derivation as described here is needed for a further generalization to a kinetic equation that includes mode-coupling effects. This will be presented in a future paper.
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References
J. R. Dorfman and E. G. D. Cohen,Phys. Rev. A 6:776 (1972);Phys. Rev. A 12:292 (1975).
M. C. Marchetti and T. R. Kirkpatrick,J. Stat. Phys. (1985), to appear.
R. Balescu,Phys. Fluids 3:52 (1962); see also R. Balescu, inEquilibrium and Nonequilibrium Statistical Mechanics (Wiley-Interscience, New York, 1975), pp. 630–643, and references therein.
J. T. Bartis and I. Oppenheim,Phys. Rev. A 8:3174 (1973).
R. L. Guernsey, inLectures in Theoretical Physics, Kinetic Theory, Vol. IXC, W. E. Brittin, ed., (Gordon and Breach, New York, 1967), pp. 147–169.
J. Krommes and C. Oberman,J. Plasma Phys. 16:193 (1976).
M. Baus,Physica 79A:377 (1975).
H. Gould and G. F. Mazenko,Phys. Rev. A 15:1274 (1977).
M. Baus and J. Wallenborn,J. Stat. Phys. 16:91 (1977).
J. L. Lebowitz, J. K. Percus, and J. Sykes,Phys. Rev. 188:487 (1969).
M. Baus and J. P. Hansen,Phys. Rep. 59:1 (1980).
J. R. Dorfman and E. G. D. Cohen,Int. J. Quant. Chem. 16:63 (1982).
J. E. Mayer and M. Goeppert-Mayer,Statistical Mechanics, 2nd ed. (Wiley, New York, 1977), Chap. 8.
J. P. Mondt,Ann. Phys. (Leipzig) 117:195 (1979).
R. Zwanzig,Phys. Rev. 129:486 (1963).
H. L. Friedman,Ionic Solution Theory (interscience, New York, 1962), pp. 132–137.
D. C. Montgomery and D. Tidman, inPlasma Kinetic Theory (McGraw-Hill, New York, 1964).
D. Pines and P. Nozières,The Theory of Quantum Liquids (Benjamin, New York, 1966).
T. O'Neil and N. Rostoker,Phys. Fluids 8:1109 (1965).
M. C. Marchetti, E. G. D. Cohen, T. R. Kirkpatrick, and J. R. Dorfman,J. Stat. Phys. 41:75 (1985), following paper.
G. E. Uhlenbeck and G. W. Ford, inStudies in Statistical Mechanics, Vol. I, J. de Boer and G. E. Uhlenbeck, eds. (North-Holland Publishing Co., Amsterdam, 1961), p. 123.
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Marchetti, M.C., Kirkpatrick, T.R., Dorfman, J.R. et al. Kinetic equation for a weakly interacting classical electron gas. J Stat Phys 41, 37–74 (1985). https://doi.org/10.1007/BF01020603
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DOI: https://doi.org/10.1007/BF01020603