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Journal of Statistical Physics

, Volume 11, Issue 6, pp 503–521 | Cite as

Memory function for dressed particles

  • Eugene P. Gross
Articles

Abstract

This paper is concerned with the calculation of the memory function and derivation of a kinetic equation for one-body phase space correlation functions. The theory uses a one-body additive projection operator and a division of the Liouville operator with an unperturbed part that describes dressed particles. Binary collisions are neglected, for the theory aims at describing the screening and backflow effects of a type contained in the plasma kinetic theory of Balescu and Lenard. We obtain an explicit kinetic equation which is an improvement of these theories for the plasma case, and involves the exact equilibrium pair and triplet distributions. The equation also describes systems with strong short-range forces and shows how the screening effects occur in this case as well. The unifying function is the direct correlation function. The theory is meant to provide understanding for a more complete theory of fluids where a proper account is given of close collisions.

Key words

Memory function kinetic equation dressed particles 

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References

  1. 1.
    B. J. Berne,Physical Chemistry, ed. by H. Eyring, D. Henderson, and W. Jost, Academic Press, New York (1971), Vol. VIIIB, Chapter 9.Google Scholar
  2. 2.
    J. L. Lebowitz, J. K. Percus, and J. Sykes,Phys. Rev. 188:487 (1969).Google Scholar
  3. 3.
    H. Mori,Prog. Theor. Phys. 33:423 (1965);34:399 (1965).Google Scholar
  4. 4.
    L. P. Kadanoff and J. Swift,Phys. Rev. 166:89 (1968).Google Scholar
  5. 5.
    K. Kawasaki,Ann. Phys. (N. Y.) 61:1 (1970).Google Scholar
  6. 6.
    A. Z. Akcasu and J. J. Duderstadt,Phys. Rev. 188:479 (1969); J. J. Duderstadt and A. Z. Akcasu,Phys. Rev. A 1:905 (1970).Google Scholar
  7. 7.
    R. Zwanzig,Phys. Rev. 144:170 (1966);156:190 (1967); R. Nossal and R. Zwanzig,Phys. Rev. 157:120 (1967); R. Nossal,Phys. Rev. 166:81 (1968).Google Scholar
  8. 8.
    E. P. Gross,Ann. Phys. 69:42 (1972);J. Stat. Phys. 9:275, 294 (1973).Google Scholar
  9. 9.
    K. Bergeron, E. P. Gross, and R. Varley,J. Stat. Phys. 10:111 (1974).Google Scholar
  10. 10.
    R. Balescu,Statistical Mechanics of Charged Particles, Wiley, London (1963); T. Y. Wu,Kinetic Equations of Gases and Plasmas, Addison Wesley, Reading, Massachusetts (1966); Y. L. Klimontovich,The Statistical Theory of Nonequilibrium Processes in Plasmas, Pergamon Press, New York (1967); S. Ichimaru,Basic Principles of Plasma Physics, Benjamin, Reading, Massachusetts (1973).Google Scholar
  11. 11.
    D. Forster and P. C. Martin,Phys. Rev. A 2:1575 (1970); D. Forster, Thesis, Harvard University (1969); D. Forster,Phys. Rev. A 9:943 (1974).Google Scholar
  12. 12.
    R. L. Guernsey,Phys. Rev. 5:322 (1962).Google Scholar
  13. 13.
    I. Prigogine,Non-Equilibrium Statistical Mechanics, Interscience Publishers, New York (1962).Google Scholar
  14. 14.
    A. Z. Akcasu,Phys. Rev. A 7:182 (1973).Google Scholar
  15. 15.
    G. F. Mazenko,Phys. Rev. A 9:360 (1974);3:2121 (1971);5:2545 (1972), and references therein; C. D. Boley and R. C. Desai,Phys. Rev. A 7:1700 (1973);7:2192 (1973).Google Scholar
  16. 16.
    C. D. Boley, preprint, in press.Google Scholar
  17. 17.
    T. H. Dupree,Phys. Fluids 4:696 (1961).Google Scholar
  18. 18.
    K. Bergeron, Ph.D. thesis, Brandeis University (October 1974).Google Scholar
  19. 19.
    E. P. Gross and K. Bergeron, to be published.Google Scholar

Copyright information

© Plenum Publishing Corporation 1974

Authors and Affiliations

  • Eugene P. Gross
    • 1
  1. 1.Department of PhysicsBrandeis UniversityWaltham

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