  We solve the time evolution of the density matrix both for fermions and
bosons in the presence of a homogeneous but time dependent external electric
field. The number of particles produced by the external field, as well as their
distribution in momentum space is found for finite times. Furthermore, we
calculate the probability of finding a given number of particles in the
ensemble. In all cases, there is a nonvanishing thermal contribution. The
bosonic and the fermionic density matrices are expressed in a "functional field
basis". This constitutes an extension of the "field basis" concept to fermions.
