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Long-time tails of the velocity autocorrelation functions for the triangular periodic Lorentz gas

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Abstract

We present numrical results on the velocity autocorrelation function (VACF)C(t)=<ν(t)·ν(0)> for the periodic Lorentz gas on a two-dimensional triangular lattice as a function of the radiusR of the hard disk scatterers on the lattice. Our results for the unbounded horizon case\((0< R< \sqrt 3 /4)\) confirm 1/t decay of the VACF for long times (out to 100 times the mean free time between collisions) and provide strong support for the conjecture by Friedman and Martin that the 1/t decay is due to long free paths along which a moving particle does not scatter up to timet. Even after new sets of long free paths become available forR<1/4, we continue to find good agreement between numerical results and an analytically estimated 1/t decay. For the bounded horizon case\((\sqrt 3 /4 \leqslant R \leqslant 0.5)\), our numerical VACFs decay exponentially, although it is difficult to discriminate among pure exponential decay, exponential decay with prefactor, and stretched exponential decay.

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Authors and Affiliations

  1. Department of Physics, Illinois State University, 61790-4560, Normal, Illinois

    H. Matsuoka & R. F. Martin Jr.

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  1. H. Matsuoka
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  2. R. F. Martin Jr.
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Matsuoka, H., Martin, R.F. Long-time tails of the velocity autocorrelation functions for the triangular periodic Lorentz gas. J Stat Phys 88, 81–103 (1997). https://doi.org/10.1007/BF02508465

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  • DOI: https://doi.org/10.1007/BF02508465

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