Boltzmann Limit and Quasifreeness for a Homogenous Fermi Gas in a Weakly Disordered Random Medium |
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Authors: | Thomas Chen Itaru Sasaki |
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Institution: | (1) Department of Mathematics, Princeton University, Princeton, NJ 08544, USA;(2) Department of Mathematics, University of Texas at Austin, Austin, TX, USA |
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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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Keywords: | Fermi gas Quantum dynamics in random medium Boltzmann limit Quasifreeness |
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