  We show that quantum effects dramatically enhance the production of fermions
following preheating after inflation in the early Universe in the presence of
high excitations of bosonic quanta. As a consequence fermions rapidly approach
a quasistationary distribution with a thermal occupancy in the infrared, while
the inflaton enters a turbulent scaling regime. The failure of standard
semiclassical descriptions based on the Dirac equation with a homogeneous
background field is caused by nonperturbatively high boson occupation numbers.
During preheating the inflaton occupation number increases, thus leading to a
dynamical mechanism for the enhanced production of fermions from the
rescattering of the inflaton quanta. We comment on related phenomena in
heavy-ion collisions for the production of quark matter fields from highly
occupied gauge bosons.
