Two-time electron-LO-phonon quantum kinetics and the generalized Kadanoff-Baym approximation

We solve numerically the time-dependent self-consistent random phase approximation Dyson equations for a system of electrons and holes of a direct gap semiconductor excited by an ultrashort laser pulse interacting with LO phonons in equilibrium. Special care is devoted to the proper treatment of the prehistory of the system by including the polaron effects. We show that for weak Fröhlich coupling $(\alpha =0.1),$ the generalized Kadanoff-Baym relationship, which enables a one-time formulation, is excellently verified while for intermediate coupling $(\alpha =1)$ the deviations become important.