Long quantum transition times due to unstable semiclassical dynamics

TL;DR

This paper explores how unstable semiclassical trajectories lead to long and asymmetric quantum transition times across various processes, revealing universal and distinctive behaviors in transition-time distributions.

Contribution

It demonstrates that unstable semiclassical trajectories cause prolonged and asymmetric transition times, providing detailed analysis across tunneling, activation, and over-barrier processes.

Findings

Transition durations are significantly longer for unstable trajectories.

Transition-time distributions exhibit asymmetric and universal forms.

Long-time asymptotics are governed by trajectories near the barrier top.

Abstract

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.