  We study the exact dynamics of a one-dimensional spin-polarized gas of
fermions in a double-well potential at zero and finite temperature. Despite the
system is made of non-interacting fermions, its dynamics can be quite complex,
showing strongly aperiodic spatio-temporal patterns during the tunneling. The
extension of these results to the case of mixtures of spin-polarized fermions
in interaction with self-trapped Bose-Einstein condensates (BECs) at zero
temperature is considered as well. In this case we show that the fermionic
dynamics remains qualitatively similar to the one observed in absence of BEC
but with the Rabi frequencies of fermionic excited states explicitly depending
on the number of bosons and on the boson-fermion interaction strength. From
this, the possibility to control quantum fermionic dynamics by means of
Feshbach resonances is suggested.
