Signatures of unstable semiclassical trajectories in tunneling

TL;DR

This paper investigates how unstable semiclassical trajectories influence multidimensional tunneling, revealing new power-law behaviors and broader probability distributions, supported by a first-principles semiclassical approach.

Contribution

It introduces a modified semiclassical technique to analyze unstable trajectories and derives explicit expressions for tunneling probabilities, advancing understanding of tunneling dynamics.

Findings

Unstable trajectories cause a power-law dependence in tunneling probability.

Probability distributions over final states are significantly widened.

Established a relation between tunneling probabilities from different initial states.

Abstract

It was found recently that processes of multidimensional tunneling are generally described at high energies by unstable semiclassical trajectories. We study two observational signatures related to the instability of trajectories. First, we find an additional power-law dependence of the tunneling probability on the semiclassical parameter as compared to the standard case of potential tunneling. The second signature is substantial widening of the probability distribution over final-state quantum numbers. These effects are studied using modified semiclassical technique which incorporates stabilization of the tunneling trajectories. The technique is derived from first principles. We obtain expressions for the inclusive and exclusive tunneling probabilities in the case of unstable semiclassical trajectories. We also investigate the "phase transition" between the cases of stable and unstable trajectories across certain "critical" value of energy. Finally, we derive the relation between the semiclassical probabilities of tunneling from the low-lying and highly excited initial states. This puts on firm ground a conjecture made previously in the semiclassical description of collision-induced tunneling in field theory.