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Classical and quantum transport in random media. (English) Zbl 1035.82037

Authors’ abstract: We consider the general problem of transport of particles in a time-dependent random medium. It is shown that the Liouville equation converges to a Fokker-Planck equation. It is also shown that the semiclassical limit of a Schrödinger equation is described by a linear Boltzmann equation. In both cases the ratio between a typical time-scale and the time-scale of the media determines whether the limit diffusion and the collision process are elastic or not.

MSC:

82C70 Transport processes in time-dependent statistical mechanics
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
82C40 Kinetic theory of gases in time-dependent statistical mechanics
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