Temporally and spatially resolved electron-phonon quantum kinetics

A quantum kinetic theory that is able to resolve interaction processes betw een carriers and phonons in time and in space is presented. The dynamics of spatially localized wave-packets is analyzed accounting for coherent as we ll as incoherent phonons. It is found that, as a consequence of the energy- time uncertainty, a fast initial carrier transport takes place leading to o ccupations of space regions which are out of reach at early times within a semiclassical description on the level of the Boltzmann equation. The charg e separation that accompanies the transport of electrons is a source of coh erent phonons. The corresponding polarizations of the ion-lattice show osci llations that form a spatially expanding wavefront. Adding incoherent phono ns leads to a damping of these waves due to phonon-assisted carrier redistr ibutions.