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Boltzmann Limit and Quasifreeness for a Homogenous Fermi Gas in a Weakly Disordered Random Medium

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Abstract

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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Authors and Affiliations

  1. Department of Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Thomas Chen & Itaru Sasaki

  2. Department of Mathematics, University of Texas at Austin, Austin, TX, USA

    Thomas Chen

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  1. Thomas Chen
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  2. Itaru Sasaki
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Correspondence to Thomas Chen.

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Chen, T., Sasaki, I. Boltzmann Limit and Quasifreeness for a Homogenous Fermi Gas in a Weakly Disordered Random Medium. J Stat Phys 132, 329–353 (2008). https://doi.org/10.1007/s10955-008-9560-9

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  • DOI: https://doi.org/10.1007/s10955-008-9560-9

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