  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. Third, we investigate long-time asymptotics of transition-time
distributions in the case of over-barrier wave packet transmissions. We show
that behavior of these asymptotics is controlled by unstable semiclassical
trajectories which linger near the barrier top.
