Computer simulations of long-time tails: what's new?

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    Abstract

    Twenty five years ago Alder and Wainwright discovered, by simulation, the ‘long-time tails’ in the velocity autocorrelation function of a single particle in fluid [1]. Since then, few qualitatively new results on long-time tails have been obtained by computer simulations. However, within the framework of a lattice gas simulation, we recently developed a technique that makes it possible to ‘measure’ such velocity autocorrelation functions with an efficiency that is at least a factor 106 higher than can be achieved with conventional techniques. This method opens the way for making comparisons with the predictions of mode-coupling theory of long-time tails, to an accuracy which was hitherto not possible. In this paper we describe this method, and review the results on long-time tails that have been obtained. In particular, we present evidence that the functional form of the long-time tail in a two-dimensional fluid is qualitatively different from the simple power law observed by Alder-Wainwright. Such ‘faster-than-t −1’ decay is in agreement with the predictions of ‘self-consistent’ mode-coupling theory.
    Original languageEnglish
    Pages (from-to)1227-1247
    Number of pages21
    JournalTransport theory and statistical physics
    Volume24
    Issue number6-8
    DOIs
    Publication statusPublished - 1995

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