ar X iv : c on d - m at / 9 70 31 05 v 1 1 1 M ar 1 99 7 Hot electron relaxation : Exact solution for a many electron model

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.