Journal of Statistical Physics

, Volume 33, Issue 2, pp 261–286 | Cite as

Mode coupling from linear and nonlinear kinetic equations

  • James W. Dufty
  • Rosalío F. Rodríguez
Articles

Abstract

The calculation of mode coupling contributions to equilibrium time correlation functions from the nonlinear Boltzmann equation is reconsidered. It is suggested that the use of a nonlinear kinetic equation is not appropriate in this context, but instead such calculations should be reinterpreted in terms of the Klimontovich equation for the microscopic phase space density. For hard spheres the Klimontovich equation is formally similar to the nonlinear Boltzmann equation, and this similarity is exploited to explain the successful calculation of mode coupling effects from the latter. The relationship of the Klimontovich formulation to the linear ring approximation is also established.

Key words

Kinetic equation Klimontovich equation time correlation functions mode coupling hard spheres nonlinear dynamics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. R. Dorfman and E. G. D. Cohen,Phys. Rev. A 6:776 (1972), and references therein.Google Scholar
  2. 2.
    E. H. Hauge,Phys. Rev. Lett. 28:1501 (1972).Google Scholar
  3. 3.
    B. I. Sadovnikov and N. G. Inozemtseva,Physica 94A:615 (1978).Google Scholar
  4. 4.
    G. W. Ford, inThe Boltzmann Equation, E. G. D. Cohen and W. Thirring, eds. (Springer Verlag, Vienna, 1973).Google Scholar
  5. 5.
    J. T. Ubbink and E. Hauge,Physica 70:297 (1973).Google Scholar
  6. 6.
    E. G. D. Cohen, inFundamental Problems in Statistical Mechanics, E. G. D. Cohen, ed. (North-Holland, Amsterdam, 1968).Google Scholar
  7. 7.
    M. H. Ernst and J. R. Dorfman,Physica 61:157 (1972).Google Scholar
  8. 8.
    J. L. Lebowitz, J. K. Percus, and J. Sykes,Phys. Rev. 188:487 (1969).Google Scholar
  9. 9.
    K. Yosida,Functional Analysis (Springer Verlag, Berlin, 1978).Google Scholar
  10. 10.
    J. A. McLennan,J. Stat. Phys. 28:257 (1982); Nonequilibrium Statistical Mechanics, Lehigh University Lecture Notes.Google Scholar
  11. 11.
    H. H. U. Konijnendijk and J. M. J. van Leeuwen,Physica 64:342 (1973).Google Scholar
  12. 12.
    Y. L. Klimontovich,Sov. Phys. JETP 6:753 (1958);The Statistical Theory of Nonequilibrium Processes in a Plasma (MIT Press, Cambridge, Massachusetts, 1967).Google Scholar
  13. 13.
    A. A. Vlasov,Many Particle Theory (in Russian) (Gostekhizdat, Moscow, 1950).Google Scholar
  14. 14.
    S. Tsuge and K. Sagara,J. Stat. Phys. 12:403 (1975); N. N. Bogoliubov,Theor. Math. Fiz. 24:242 (1975).Google Scholar
  15. 15.
    M. H. Ernst, J. R. Dorfman, W. R. Hoegy, and J. M. J. van Leeuwen,Physica 45:129 (1969).Google Scholar
  16. 16.
    M. H. Ernst and E. G. D. Cohen,J. Stat. Phys. 25:153 (1981).Google Scholar
  17. 17.
    A. Z. Akcasu and J. J. Duderstadt,Phys. Rev. 188:479 (1969).Google Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • James W. Dufty
    • 1
  • Rosalío F. Rodríguez
    • 1
  1. 1.Thermophysics DivisionNational Bureau of StandardsWashington, D.C.

Personalised recommendations