Numerical calculation of transient excitonic Green functions in the presence of phonon scattering

Abstract

As a demonstration of the growing feasiblity of quantum treatment of complex systems with parallel computing we have performed a transient population dynamics calculation for carriers interacting via Coulomb and electron-phonon interactions. Two-point Keldysh functions are obtained by integrating the Dyson equation in the time domain. Keldysh functions are treated explicitly as matrices with discretized real time as their index in order to be able to deal squarely with fast transient phenomena. The Coulomb interaction is included in the electron self-energy within the Hartree-Fock approximation, while the interaction with localized non-dispersive thermal phonons is taken into account up to the second order in the electron-phonon vertex. The numerical procedure is applied to the case of carrier excitation by an ultrashort laser pulse in a model two-band semiconductor to obtain the transient behaviour of carrier population and the luminescence spectrum shortly after the excitation.