Time-linear quantum transport simulations with correlated nonequilibrium Green's functions

We present a time-linear scaling method to simulate open and correlated quantum systems. The method inherits from many-body perturbation theory the possibility to choose selectively the most relevant scattering processes in the dynamics, thereby paving the way to the real-time characterization of correlated ultrafast phenomena in quantum transport. The open system dynamics is described in terms of an embedding correlator from which the time-dependent current can be calculated using the Meir-Wingreen formula. We show how to efficently implement the method through a simple grafting into recently proposed time-linear Green's function schemes for closed systems. Electron-electron and electron-phonon interactions can be treated on equal footing while preserving all fundametal conservation laws.