Thomas Chen, Itaru Sasaki
Boltzmann limit and quasifreeness for a homogenous Fermi gas in
a weakly disordered random medium
(402K, AMS Latex, 26 pages, 2 figures.)
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.