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From the Liouville Equation to the Generalized Boltzmann Equation for Magnetotransport in the 2D Lorentz Model

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Abstract

We consider a system of non-interacting charged particles moving in two dimensions among fixed hard scatterers, and acted upon by a perpendicular magnetic field. Recollisions between charged particles and scatterers are unavoidable in this case. We derive from the Liouville equation for this system a generalized Boltzmann equation with infinitely long memory, but which still is analytically solvable. This kinetic equation has been earlier written down from intuitive arguments.

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Authors and Affiliations

  1. Department of Physics, Norwegian University of Science and Technology, N-7491, Trondheim, Norway

    A. V. Bobylev & E. H. Hauge

  2. Laboratoire de Physique de l'Ecole Normale Supérieure de Lyon, F-69364, Lyon Cedex 07, France

    Alex Hansen

  3. Institute of Theoretical Physics, University of Warsaw, ul. Hoża 69, PL-00 681, Warsaw, Poland

    J. Piasecki

Authors
  1. A. V. Bobylev
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  2. Alex Hansen
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  3. J. Piasecki
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  4. E. H. Hauge
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Bobylev, A.V., Hansen, A., Piasecki, J. et al. From the Liouville Equation to the Generalized Boltzmann Equation for Magnetotransport in the 2D Lorentz Model. Journal of Statistical Physics 102, 1133–1150 (2001). https://doi.org/10.1023/A:1004880010020

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  • DOI: https://doi.org/10.1023/A:1004880010020

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