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1 results

  • 5 - The Dilute Lorentz Gas

  • J. R. Dorfman, University of Maryland, College Park, Henk van Beijeren, Universiteit Utrecht, The Netherlands, T. R. Kirkpatrick, University of Maryland, College Park
  • Book:
    Contemporary Kinetic Theory of Matter
    Published online:
    18 June 2021
    Print publication:
    24 June 2021, pp 149-204

  • Summary

    The Lorentz model consists of non-interacting, point particles moving among a collection of fixed scatterers of radius a, placed at random, with or without overlapping, at density n 6 in space. This model was designed to be, and serves as, a model for the motion of electrons in solids. The kinetic equation for the moving particles must be linear, and for low scatterers density, nad >> 1, it is the Lorentz-Boltzmann equation. If external fields are absent, the Chapman-Enskog method leads to the diffusion equation. For three dimensional systems with hard sphere scatterers, the Lorentz-Boltzmann equation can be solved exactly, and the range of validity of the Chapman-Enskog solution can be examined. Electrical conduction and magneto-transport can be studied for charged, moving particles. In both cases there are unexpected results. The Lorentz model with hard sphere scatterers is a chaotic system, and one can calculate Lyapunov exponents and related dynamical quantities.