Long transient dynamics in the Anderson-Holstein model out of equilibrium

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We calculate the time dependent nonequilibrium current through a single level quantum dot strongly coupled to a vibrational mode. The nonequilibrium real time dynamics caused by an instantaneous coupling of the leads to the quantum dot is discussed using an approximate method. The approach, which is specially designed for the strong polaronic regime, is based on the so-called polaron tunneling approximation. Considering different initial dot occupations, we show that a common steady state is reached after times much larger than the typical electron tunneling times due to a polaron blocking effect in the dot charge. A direct comparison is made with numerically exact data, showing good agreement for the time scales accessible by the diagrammatic Monte Carlo simulation method.