Journal of Statistical Physics

, Volume 12, Issue 4, pp 311–359 | Cite as

Nonanalytic dispersion relations for classical fluids

II. The general fluid
  • M. H. Ernst
  • J. R. Dorfman


The analytic structure of the hydrodynamic frequenciesz(k) for the sound, heat, and shear modes and of the hydrodynamic equations for a monatomic fluid are discussed on the basis of the mode-mode coupling theory. It is shown that the hydrodynamic frequencies depend on the wave numberk, for smallk, asz(k) = ak + bk2 +\(z(k) = ak + bk^2 + \sum\nolimits_{n = 1}^\infty {c_n k^{3 - 2^{ - n} } } \) and that some of the correlation functions that appear in the Fourier-Laplace transforms of the hydrodynamic equations contain branch point singularities. The implications of these results for the derivation of linear hydrodynamic equations, such as the Burnett equations, and for the long-time behavior of time correlation functions are discussed.

Key words

Statistical mechanics nonequilibrium statistical mechanics hydrodynamic equations Navier-Stokes equations Burnett equations time correlation functions 


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Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • M. H. Ernst
    • 1
  • J. R. Dorfman
    • 2
  1. 1.Institute for Theoretical PhysicsUniversity of UtrechtThe Netherlands
  2. 2.Institute for Fluid Dynamics and Applied Mathematics, and Department of Physics and AstronomyUniversity of MarylandMaryland

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