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Real time electron dynamics in an interacting vibronic molecular quantum dot

We employ the time-dependent non-crossing approximation to investigate the joint effect of strong electron-electron and electron-phonon interaction on the instantaneous conductance of a single molecule transistor which is abruply moved into the Kondo regime by means of a gate voltage. We find that the instantaneous conductance exhibits decaying sinusoidal oscillations in the long timescale for infinitesimal bias. Ambient temperature and electron-phonon coupling strength influence the amplitude of these oscillations. The frequency of oscillations is found to be equal to the phonon frequency. We argue that the origin of these oscillations can be attributed to the interference between the emerging Kondo resonance and its phonon sidebands. We discuss the effect of finite bias on these oscillations.