Abstract
We introduce and analyse a new and special case of the Lorentz gas or the Wind-Tree model of Ehrenfest. This model (which has a number-theoretic character) is shown to exhibit normal diffusion, the diffusion coefficient C(ϱ) being obtained in closed form as a function of the density ϱ. The function ϱ C(ϱ) turns out to be an entire analytic function of ϱ, in spite of the model's non-classical high density behaviour. A “collision expansion” which is appropriate for high densities is also given.
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Gallavotti, G. & D.S. Ornstein, to appear in Commun. Math. Phys.
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Communicated by J. Serrin
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Gates, D.J. An exactly solvable Lorentz gas. Arch. Rational Mech. Anal. 61, 175–185 (1976). https://doi.org/10.1007/BF00249704
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DOI: https://doi.org/10.1007/BF00249704