BBGKY-Approach to non{Markovian Semiconductor Bloch Equations

A density operator approach to generalized semiconductor Bloch equations (SBE) for one-time observables which includes carrier±carrier scattering effects is presented. The theoretical concept is based upon the quantum generalization of the BBGKY hierarchy for the reduced density operators. The advantage of our method is its simplicity and transparence ± to a large extent, derivations and physical approximations can be performed on the simplest level possible, that of a one-component system of spinless particles. We discuss various approximations for the incoherent terms in the Bloch equations which are related to carrier±carrier correlations, such as strong coupling effects and the build-up of dynamical screening as well as self-energy effects. As a result we obtain nonMarkovian generalizations of the SBE.