  We study the macroscopic quantum self-trapping effect in a mixture of
Bose-Einstein condensate and a large number of quantum degenerate fermions,
trapped in a double-well potential with a variable separation between the
wells. The large number of fermions localized in each well form quasi-static
impurities that affect the dynamics of the bosonic cloud. Our semi-analytical
analysis based on a mean-field model shows that main features of macroscopic
quantum self trapping in a pure bosonic system are radically modified by the
influence of fermions, with both the onset of self-trapping and properties of
the self-trapped state depending on the fermion concentration as well as on the
type of inter-species interaction. Remarkably, repulsive inter-species
interaction leads to population inversion of the bosonic energy levels in the
trapping potential and hence to the inversion of symmetry of the macroscopic
wavefunction. Realistic physical estimates are given based on experimental
parameters for a $^{40}$K-$^{87}$Rb system.
