  We present a theoretical study of the dynamical behavior of a gas made of
ultracold fermionic atoms, which during their motions can collide with a much
smaller number of thermal bosonic impurities. The atoms are confined inside
harmonic traps and the interactions between the two species are treated as due
to s-wave scattering with a negative scattering length modeling the 40K-87Rb
fermion-boson system. We set the fermions into motion by giving a small shift
to their trap center and examine two alternative types of initial conditions,
referring to (i) a close-to-equilibrium situation in which the two species are
at the same temperature (well below the Fermi temperature and well above the
Bose-Einstein condensation temperature); and (ii) a far-from-equilibrium case
in which the impurities are given a Boltzmann distribution of momenta while the
fermions are at very low temperatures. The dynamics of the gas is evaluated by
the numerical solution of the Vlasov-Landau equations for the one-body
distribution functions, supported by some analytical results on the collisional
properties of a fermion gas. We find that the trapped gaseous mixture is close
to the collisionless regime for values of the parameters corresponding to
current experiments, but can be driven towards a collisional regime even
without increasing the strength of the interactions, either by going over to
heavier impurity masses or by matching the width of the momentum distribution
of the impurities to the Fermi momentum of the fermion gas.
