Journal of Statistical Physics

, Volume 51, Issue 5–6, pp 981–990 | Cite as

Lorentz lattice gases: Basic theory

  • M. H. Ernst
  • P. M. Binder


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.

Key words

Lorentz gas lattice gases Liouville equation Boltzmann equation diffusion coefficient 


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Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • M. H. Ernst
    • 1
    • 2
  • P. M. Binder
    • 2
    • 3
    • 4
  1. 1.Institute for Theoretical PhysicsState UniversityTA UtrechtThe Netherlands
  2. 2.Los Alamos National LaboratoryCenter for Nonlinear Studies, MS-B258Los Alamos
  3. 3.Applied Physics SectionYale UniversityNew Haven
  4. 4.Groupe de Physique des SolidesÉcole Normale SupérieureParisFrance

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