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Long quantum transitions due to unstable semiclassical dynamics

Quantum transitions are described semiclassically as motions of systems along (complex) trajectories. We consider the cases when the semiclassical trajectories are unstable and find that durations of the corresponding transitions are large. In addition, we show that the probability distributions over transition times have unusual asymmetric form in cases of unstable trajectories. We investigate in detail three types of processes related to unstable semiclassical dynamics. First, we analyze recently proposed mechanism of multidimensional tunneling where transitions proceed by formation and subsequent decay of classically unstable “states.” The second class of processes includes one–dimensional activation transitions due to energy dispersion. In this case the semiclassical transition–time distributions have universal form; we compare them with exact distributions and find agreement. Third, we investigate long–time asymptotics of transition–time distributions in the case of over–barrier wave packet transmissions. We show that the behavior of these asymptotics is controlled by unstable semiclassical trajectories which linger near the barrier top.