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Journal of Statistical Physics

Boltzmann Limit for a Homogeneous Fermi Gas with Dynamical Hartree-Fock Interactions in a Random Medium

Thomas Chen, Igor Rodnianski

Published Feb 14, 2011• 5 citations
Publisher
DOI
10.1007/s10955-011-0145-7

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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.