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Asymptotic motion of a classical particle in a random potential in two dimensions: Landau model

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Abstract

We consider the motion of a classical particle in a random isotropic potential arising from uniformly distributed scatterers in two dimensions. We prove that in the weak coupling limit the velocity process of the particle converges in distribution to Brownian motion on a surface of constant speed, i.e. on the circle. The resulting equation for the probability density of the particle is related to the Landau equation in plasmas.

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Authors and Affiliations

  1. Fachbereich Mathematik, Ruhr Universität Bochum, Bochum, FRG

    Detlef Dürr (Heisenberg fellow)

  2. Department of Mathematics, Rutgers University, 08903, New Brunswick, New Jersey, USA

    Sheldon Goldstein & Joel L. Lebowitz

  3. BiBoS Universität Bielefeld, Bielefeld

    Detlef Dürr (Heisenberg fellow)

Authors
  1. Detlef Dürr
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  2. Sheldon Goldstein
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  3. Joel L. Lebowitz
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Additional information

Communicated by M. Aizenman

also: Department of Physics

Work supported in part by National Science Foundation Grant No. DMS-85-12505 and AFOSR No. C010

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Dürr, D., Goldstein, S. & Lebowitz, J.L. Asymptotic motion of a classical particle in a random potential in two dimensions: Landau model. Commun.Math. Phys. 113, 209–230 (1987). https://doi.org/10.1007/BF01223512

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  • DOI: https://doi.org/10.1007/BF01223512

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