  We analyze the time evolution describing a quantum source for noninteracting
particles, either bosons or fermions. The growth behaviour of the particle
number (trace of the density matrix) is investigated, leading to spectral
criteria for sublinear or linear growth in the fermionic case, but also
establishing the possibility of exponential growth for bosons. We further study
the local convergence of the density matrix in the long time limit and prove
the semiclassical limit.
