Boltzmann limit and quasifreeness for a homogenous Fermi gas in a weakly disordered random medium

Details Boltzmann limit and quasifreeness for a homogenous Fermi gas in a weakly disordered random medium Boltzmann limit and quasifreeness for a homogenous Fermi gas in a weakly disordered random medium

2007-11-06

arxiv.org/abs/0711.0959v3

Journal of Statistical Physics, 132 (2), 329 - 353, 2008.

Physics

Mathematical Physics

AMS Latex, 26 pages. 2 figures. References added, minor typos corrected

Scientific paper

10.1007/s10955-008-9560-9

We discuss some basic aspects of the dynamics of a homogenous Fermi gas in a weak random potential, under negligence of the particle pair interactions. We derive the kinetic scaling limit for the momentum distribution function with a translation invariant initial state and prove that it is determined by a linear Boltzmann equation. Moreover, we prove that if the initial state is quasifree, then the time evolved state, averaged over the randomness, has a quasifree kinetic limit. We show that the momentum distributions determined by the Gibbs states of a free fermion field are stationary solutions of the linear Boltzmann equation; this includes the limit of zero temperature.

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