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1 results

  • 13 - Long-Time Tails

  • J. R. Dorfman, University of Maryland, College Park, Henk van Beijeren, Universiteit Utrecht, The Netherlands, T. R. Kirkpatrick, University of Maryland, College Park
  • Book:
    Contemporary Kinetic Theory of Matter
    Published online:
    18 June 2021
    Print publication:
    24 June 2021, pp 507-540

  • Summary

    Time correlation functions appearing in the Green-Kubo expressions for transport coefficients are studied by using kinetic theory. Of particular interest is the theory for the algebraic, t??d=2 long time time decays, or long time tails, first seen in computer simulations of the velocity autocorrelation function for tagged particle diffusion. Kinetic equations for distribution functions that determine time correlation functions are obtained using cluster expansions, and divergences appear due to the effects of correlated sequences of binary collisions. The ring resummation introduced in Chapter 12 leads to mode-coupling expressions containing products of two hydrodynamic mode eigenfunctions. The sum of these contributions leads directly to the long time tails, quantitatively in agreement with computer simulations. Mode coupling theory also leads to an explanation of the observed, intermediate time, molasses tails, and to the existence of fractional powers in sound dispersion relations, for which there is strong experimental evidence.