HOT-ELECTRON RELAXATION - AN EXACTLY SOLVABLE MODEL AND IMPROVED QUANTUM KINETIC-EQUATIONS

We present a one-dimensional microscopic model of interacting electron s coupled to phonons that allows the exact calculation of the time evo lution of the momentum distribution functions starting from a nonequil ibrium initial state. The model shows relaxation features known from a pproximate calculations for more realistic three-dimensional models. T he exact results are compared with approximate ones resulting from the use of quantum kinetic equations which avoid the assumption of comple ted successive scattering processes implicit in simple Boltzmann equat ions. To renormalize the electronic but not the phonon propagation in the non-Markovian equations yields no improvement uniform in time comp ared to simpler approximations. Due to the presence of the Fermi sea o nly the additional renormalization of the phonon propagation leads to a drastic improvement in comparison with the exact results.