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arXiv:0711.0959 · Journal of Statistical Physics

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

Thomas Chen, Itaru Sasaki

Published May 13, 2008• 3 citations
arXivHTMLPDF
DOI
10.1007/s10955-008-9560-9

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Abstract. In this note, we discuss some basic aspects of the dynamics of a homogenous Fermi gas in a weak random potential, under simplifying assumptions on the particle pair interactions. We are particularly interested in studying the delocalizing effects due to the Pauli principle. We derive the kinetic hydrodynamic limit, determined by a linear Boltzmann equation, for the momentum distribution function. Moreover, we prove that if the initial state is quasifree, then the time evolved state averaged over the randomness, which is by itself not quasifree, has a quasifree hydrodynamic limit. We show that the momentum distributions determined by the Gibbs states of a free fermion field persist into the diffusive time scale; this includes the limit of zero temperature. 1.
We study the dynamics of the thermal momentum distribution function for an interacting, homogenous Fermi gas on Z3\Z^3Z3 in the presence of an external weak static random potential, where the pair interactions between the fermions are modeled in dynamical Hartree-Fock theory. We determine the Boltzmann limits associated to different scaling regimes defined by the size of the random potential, and the strength of the fermion interactions.
We theoretically study the dipole oscillations of an ideal Fermi gas in a disordered trap. We show that even weak disorder induces strong damping of the oscillations and we identify a metal-insulator crossover. For very weak disorder, we show that damping results from a dephasing effect related to weak random perturbations of the energy spectrum. For increasing disorder, we show that the Fermi gas crosses over to an insulating regime characterized by strong damping due to the proliferation of localized states.