Abstract
Diffusive behavior in various Lorentz lattice gases, especially wind-tree-like models, is discussed. Comparisons between lattice and continuum models as well as deterministic and probabilistic models are made. In one deterministic model, where the scatterers behave like double-sided mirrors, a new kind of abnormal diffusion is found, viz., the mean square displacement is proportional to the time, but the probability density distribution function is non-Gaussian. The connections of this mirror model with the percolation problem and the statistics of polymer chains on a lattice are also discussed.
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Kong, X.P., Cohen, E.G.D. Lorentz lattice gases, abnormal diffusion, and polymer statistics. J Stat Phys 62, 1153–1171 (1991). https://doi.org/10.1007/BF01128181
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DOI: https://doi.org/10.1007/BF01128181