Unstable Semiclassical Trajectories in Tunneling

TL;DR

This paper develops a systematic method to stabilize unstable semiclassical trajectories in tunneling phenomena, enabling accurate calculation of tunneling probabilities and revealing how instability affects the prefactor's dependence on Planck's constant.

Contribution

A novel systematic procedure to stabilize unstable semiclassical tunneling trajectories and compute both suppression exponents and prefactors.

Findings

Instability alters the power-law dependence of the tunneling prefactor on Planck's constant.

The developed method allows accurate calculation of tunneling probabilities involving unstable trajectories.

Unstable trajectories can be effectively stabilized using the proposed systematic approach.

Abstract

Some tunneling phenomena are described, in the semiclassical approximation, by unstable complex trajectories. We develop a systematic procedure to stabilize the trajectories and to calculate the tunneling probability, including both the suppression exponent and prefactor. We find that the instability of tunneling solutions modifies the power-law dependence of the prefactor on h as compared to the case of stable solutions.