Abstract
We give the results of a numerical study of the motion of a point particle in ad-dimensional array of spherical scatterers (Sinai's billiard without horizon). We find a simple universal law for the Lyapounov exponent (as a function ofd) and a stretched exponential decay for the velocity autocorrelation as a function of the number of collisions. The diffusion seems to be anomalous in this problem. Ergodicity is used to predict the shape of the probability distribution of long free paths. Physical interpretations or clues are proposed.
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Bouchaud, JP., Le Doussal, P. Numerical study of aD-dimensional periodic Lorentz gas with universal properties. J Stat Phys 41, 225–248 (1985). https://doi.org/10.1007/BF01020610
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DOI: https://doi.org/10.1007/BF01020610