Time-dependent screening of the carrier-phonon and carrier-carrier interactions in nonequilibrium systems

For a nonequilibrium electron system in semiconductors the time-dependent screened effective interaction due to longitudinal optical phonon and Coulomb scattering is derived. The polarization is described in terms of a time-dependent random-phase approximation. The nonequilibrium electron propagators are expressed in terms of the single-time density matrix by means of the genaralized Kadanoff-Baym approximation. We illustrate the theory for a femtosecond-pulse-excited semiconductor by calculating the resulting two-time-dependent interaction. Using an incomplete Fourier transformation we study the buildup of the phonon-plasmon double resonance in time as a function of the excited carrier density.