  The exact nonequilibrium time evolution of the momentum distribution for a
finite many particle system in one dimension with a linear energy dispersion
coupled to optical phonons is presented. For distinguishable particles the
influence function of the phonon bath can be evaluated also for a finite
particle density in the thermodynamic limit. In the case of fermions the exact
fulfillment of the Pauli principle involves a sum over permutations of the
electrons and the numerical evaluation is restricted to a finite number of
electrons. In the dynamics the antisymmetry of the wavefunction shows up in the
obvious Pauli blocking of momentum states as well as more subtle interference
effects. The model shows the expected physical features known from approximate
treatments of more realistic models for the relaxation in the energy regime far
from the bottom of the conduction band and provides an excellent testing ground
for quantum kinetic equations.
