Abstract
Stationary and dynamic properties of reduced density matrices can be determined from formal or approximate closures of an infinite hierarchy of equations. The local macroscopic conservation laws place weak but important constraints on the reduced density matrices which should be respected by any closure. For pairwise additive forces conditions on the closure of the one- and two-particle equations are obtained that preserve the exact functional dependence of the conserved densities and their fluxes on the reduced density matrices. To illustrate the nature of these conditions, a closure approximation suitable for a quantum gas is given, yielding an extension of the time-dependent Hartree-Fock equations for the dynamics of a nuclear fluid to include collisions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
N. N. Bogoliubov, inStudies in Statistical Mechanics, Vol. 1, G. Uhlenbeck and J. deBoer, eds. (North-Holland, Amsterdam, 1961).
J. Dorfman, inPerspectives in Statistical Mechanics, H. Raveche, ed. (North-Holland, New York, 1981).
D. Boercker and J. Dufty,Ann. Phys. (N.Y.) 119:43 (1979).
N. N. Bogoliubov,Lectures on Quantum Statistics, Vol. I (Gordon and Breach, New York, 1967).
L. Kadanoff and G. Baym,Quantum Statistical Mechanics (Benjamin, New York, 1976).
P. Grange, H. Weidenmuller, and G. Wolschin,Ann. Phys. 136:190 (1981), and references therein.
M. S. Green, L. S. Garcia-Colin, and A. Flores,Physica 32:450 (1966); M. H. Ernst,Physica 32:209 (1966).
H. S. Green and D. K. Hoffman,J. Chem. Phys. 49:2600 (1968).
G. Baym and I. Kadanoff,Phys. Rev. 124:287 (1961).
D. Forster,Phys. Rev. A 9:943 (1974).
S. T. Choh and G. E. Uhlenbeck, University of Michigan Report (1958), unpublished.
J. A. McLennan,Introduction in Nonequilibrium Statistical Mechanics (Prentice Hall, Englewood Cliffs, New Jersey, 1988).
E. G. D. Cohen and T. Berlin,Physica 26:717 (1960).
P. Martin and J. Schwinger,Phys. Rev. 115:1342 (1959).
J.-R. Buchler and B. Datta,Phys. Rev. C 19:494 (1979).
J. Dufty and D. Boercker,J. Quant. Spectrosc. Radiat. Transfer 16:1065 (1976); D. Boercker, Ph.D. thesis, University of Florida (University Microfilms, 1978).
K. Goeke and P.-G. Reinhard, eds.,Time Dependent Hartree Fock and Beyond (Springer-Verlag, New York, 1982).
H. T. Davis, S. A. Rice, and J. V. Sengers,J. Chem. Phys. 35:2210 (1961).
J. Karkheck, H. van Beijeren, I. M. de Schepper, and G. Stell,Phys. Rev. A 32:2517 (1985); H. van Beijeren, J. Karkheck, and J. V. Sengers,Phys. Rev. A 37:2247 (1988).
S. Ichimaru,Basic Principles of Plasma Physics (Benjamin, London, 1973).
M. Ernst, B. Cicchocki, J. Dorfman, J. Sharma, and H. van Beijeren,J. Stat. Phys. 18:237 (1978).
W. D. Kraeft, M. Schlanges, and D. Kremp,J. Phys. A 19:3251 (1987).
Y. L. Klimontovich, D. Kremp, and W. Kraeft,Adv. Chem. Phys. 68:175 (1987).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dufty, J.W., Boercker, D.B. Classical and quantum kinetic equations with exact conservation laws. J Stat Phys 57, 827–839 (1989). https://doi.org/10.1007/BF01022835
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01022835