Reconciling perturbative approaches in phonon-assisted transport junctions

We present consistent results for molecular conduction using two central-complementary approaches: the non-equilibrium Green's function technique and the quantum master equation method. Our model describes electronic conduction in a donor-acceptor junction in which electron transfer is coupled to nuclear motion, modeled by a harmonic vibrational mode. This primary mode is further coupled to secondary phonon modes, a thermal bath. Assuming weak electron-phonon coupling but an arbitrary large molecule-metal hybridization, we compute several non-equilibrium transport quantities: the mean phonon number of the primary mode, charge current statistics. We further present scaling relations for the cumulants valid in the large voltage regime. Our analysis illustrates that the non-equilibrium Green's function technique and the quantum master equation method can be worked out consistently, when taking into account corresponding scattering processes.