Numerical analysis of non-Markovian effects in charge-carrier scattering: One-time versus two-time kinetic equations

The non-Markovian carrier-carrier scattering dynamics in a dense electron gas is investigated. Within the framework of quantum kinetic equations in the second Born approximation we study the relevance of retardation (memory) effects, energy broadening and correlation build-up for femtosecond relaxation processes. Furthermore, the important issue of total energy conservation, within various well-established approximation schemes, is analysed. The most important non-Markovian effect is shown to be the broadening of the energy delta function leading to an increase of kinetic energy with time. Our numerical analysis includes both the single-time kinetic equation and the full two-time Kadanoff-Baym equations. Our results are expected to correctly reproduce qualitative features of non-Markovian dynamics in plasmas, fluids, nuclear matter and in the intraband relaxation of semiconductors. The comparison of the exact solutions for different approximations allows suggestions for simplifications that make this kind of calculation and their extension, especially to realistic semiconductor situations, more feasible.