Abstract
We present several ballistic models of the Lorentz gas in two-dimensional lattices with deterministic and stochastic deflection rules, and their corresponding Liouville equations. Boltzmann-level-equation results are obtained for the diffusion coefficient and velocity autocorrelation function for models with stochastic deflection rules. The long-time behavior of the mean square displacement is briefly discussed and the possibility of abnormal diffusion indicated. Even if the diffusion coefficient exists, its low-density limit may not be given correctly by the Boltzmann equation.
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Ernst, M.H., Binder, P.M. Lorentz lattice gases: Basic theory. J Stat Phys 51, 981–990 (1988). https://doi.org/10.1007/BF01014895
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DOI: https://doi.org/10.1007/BF01014895