Various velocity correlations functions in a Lorentz gas - simulation and mode coupling theory

C. P. Lowe, A. J. Masters

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We present computer simulation results for several types of velocity correlation function in the two dimensional, overlapping Lorentz gas. Only the normal velocity autocorrelation function, whose integral gives the diffusion constant, shows obvious anomalous behaviour at the percolation transition. The other functions are fairly well approximated by the Lorentz-Boltzmann equation, even for densities at which the travelling particle is trapped. We do, however, at a sub-percolation density, examine the long time behaviour of the autocorrelation function corresponding to the second rank, irreducible tensor of the velocity, and find an algebraic decay with an exponent of 3.0 ± 0.1, consistent with the theoretically expected value of 3. With these observations in mind we re-examine the mode coupling theory of Götze, Leutheusser and Yip (Phys. Rev. A 23 (1981) 2634,) replacing their one (frequency dependent) relaxation time approximation to a kinetic operator by a two (frequency dependent) relaxation time model. We find that this leads to a significantly better estimate of the diffusions constant at low density. Furthermore the theory correctly predicts no striking anomalous behaviour in the types of velocity correlation function that are unrelated to diffusion as the percolation threshold is crossed. © 1995.
    Original languageEnglish
    Pages (from-to)413-425
    Number of pages12
    JournalPhysica A: Statistical Mechanics and its Applications
    Volume214
    Issue number3
    Publication statusPublished - 15 Mar 1995

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