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Lorentz lattice gases: Basic theory

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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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Authors and Affiliations

  1. Institute for Theoretical Physics, State University, 3508, TA Utrecht, The Netherlands

    M. H. Ernst

  2. Los Alamos National Laboratory, Center for Nonlinear Studies, MS-B258, 87545, Los Alamos, New Mexico

    M. H. Ernst & P. M. Binder

  3. Applied Physics Section, Yale University, 06520, New Haven, Connecticut

    P. M. Binder

  4. Groupe de Physique des Solides, École Normale Supérieure, 75231, Paris, France

    P. M. Binder

Authors
  1. M. H. Ernst
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  2. P. M. Binder
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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

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