Abstract
Binary correlations are a recognized part of the pair density operator, but the influence of binary correlations on the singlet density operator is usually not emphasized. Here free motion and binary correlations are taken as independent building blocks for the structure of the nonequilibrium singlet and pair density operators. Binary correlations are assumed to arise from the collision of twofree particles. Together with the first BBGKY equation and a retention of all terms that are second order in gas density, a generalization of the Boltzmann equation is obtained. This is an equation for thefree particle density operator rather than for the (full) singlet density operator. The form for the pressure tensor calculated from this equation reduces at equilibrium to give the correct (Beth-Uhlenbeck) second virial coefficient, in contrast to a previous quantum Boltzmann equation, which gave only part of the quantum second virial coefficient. Generalizations to include higher-order correlations and collision types are indicated.
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References
L. Boltzmann,Wein. Ber. 66:275 (1972) (Collected Works, Vol. 1, p. 315).
L. Waldmann,Z. Naturforsch. 12a:660 (1957).
R. F. Snider,J. Chem. Phys. 32:1051 (1960).
E. Wigner,Phys. Rev. 40:479 (1932).
F. M. Chen and R. F. Snider,J. Chem. Phys. 46:3937 (1967).
R. F. Snider and B. C. Sanctuary,J. Chem. Phys. 55:1555 (1971).
M. W. Thomas and R. F. Snider,J. Stat. Phys. 2:61 (1970).
J. Yvon,J. Phys. Radium 21:569 (1960).
E. Beth and G. E. Uhlenbeck,Physica 4:915 (1937).
J. de Boer,Rep. Prog. Phys. 12:305 (1949).
J. C. Rainwater and R. F. Snider,J. Chem. Phys. 65:4958 (1976).
J. de Boer,Physica 15:680 (1949).
H. S. Green,Physica 15:882 (1949).
F. Laloé and W. J. Mullin,J. Stat. Phys. 59:725 (1990).
N. Bogolubov,J. Phys. (USSR) 10:265 (1946); Problems of a dynamical theory in statistical physics, inStudies in Statistical Physics, Vol. I, Part A, J. de Boer and G. E. Uhlenbeck, eds. (North-Holland, Amsterdam, 1962).
M. Born and H. S. Green,Proc. R. Soc. Lond. A 188:10 (1946).
J. G. Kirkwood,J. Chem. Phys. 14:180 (1946).
J. Yvon,La Théorie Statistique des Fluides et L'Equation d'Etat (Hermann, Paris, 1935).
B. Kahn, Dissertation, University of Utrecht (1938); reprinted inStudies in Statistical Mechanics, Vol. III, J. de Boer and G. E. Uhlenbeck, eds. (North-Holland, Amsterdam, 1965).
J. E. Mayer and E. W. Montroll,J. Chem. Phys. 9:2 (1941).
G. E. Uhlenbeck and G. W. Ford, inStudies in Statistical Mechanics, Vol. 1, Part B, J. de Boer and G. E. Uhlenbeck, eds. (North-Holland, Amsterdam, 1962), p. 119.
F. Laloë,J. Phys. (Paris)50:1851 (1989).
G. Tastevin, P. J. Nacher, and F. Laloë,J. Phys. (Paris)50:1879 (1989).
G. Tastevin, P. J. Nacher, and F. Laloë, inProceedings of the 3rd International Conference on Spin-Polarized Quantum Systems (Torino, Italy, 1988), S. Stringari, ed. (World Scientific, Singapore, in press).
J. T. Lowry and R. F. Snider,J. Chem. Phys. 61:2320 (1974).
H. D. Ursell,Proc. Camb. Phil. Soc. 23:685 (1927).
W. Ebeling, W. D. Kraeft, and D. Kremp,Theory of Bound States and Ionization Equilibrium in Plasmas and Solids (Akademie-Verlag, Berlin, 1976).
J. W. Essam and M. E. Fisher,Rev. Mod. Phys. 42:271 (1970).
H. S. Green,The Molecular Theory of Fluids (North-Holland, Amsterdam, 1952) [reprinted by Dover, New York, 1969].
D. H. Berman and R. F. Snider,J. Chem. Phys. 71:1740 (1979).
J. H. Irving and J. G. Kirkwood,J. Chem. Phys. 18:817 (1950).
H. J. Kreuzer,Nonequilibrium Thermodynamics and Its Statistical Foundations (Oxford University Press, Oxford, 1981).
H. Weyl,Z. Phys. 46:1 (1927).
S. Imam-Rahajoe and C. F. Curtiss,J. Chem. Phys. 47:5269 (1967).
K. E. Hawker, Ph.D. Thesis, University of Texas at Austin (1975).
E. G. D. Cohen,Physica 28:1025 (1962).
J. H. Ferziger and H. G. Kaper,Mathematical Theory of Transport Processes in Gases (North-Holland, Amsterdam, 1972).
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Snider, R.F. A density-corrected quantum Boltzmann equation. J Stat Phys 61, 443–465 (1990). https://doi.org/10.1007/BF01013975
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DOI: https://doi.org/10.1007/BF01013975