Origin of the enhancement of tunneling probability in the nearly integrable system

TL;DR

This paper investigates the origin of enhanced tunneling probabilities in nearly integrable quantum systems, revealing a staircase structure in tunneling splittings linked to anomalous tunneling tails, which is absent in fully integrable systems.

Contribution

It introduces a renormalized Hamiltonian approach and identifies the staircase structure as arising from anomalous tunneling tails, advancing understanding of tunneling phenomena in nearly integrable systems.

Findings

Tunneling splittings form a staircase-shaped pattern with spikes.

The staircase structure is linked to anomalous tunneling tails.

This structure is absent in fully integrable systems.

Abstract

The enhancement of tunneling probability in the nearly integrable system is closely examined, focusing on tunneling splittings plotted as a function of the inverse of the Planck's constant. On the basis of the analysis using the absorber which efficiently suppresses the coupling creating spikes in the plot, we found that the splitting curve should be viewed as the staircase-shaped skeleton accompanied by spikes. We further introduce renormalized integrable Hamiltonians, and explore the origin of such a staircase structure by investigating the nature of eigenfunctions closely. It is found that the origin of the staircase structure could trace back to the anomalous structure in tunneling tail which manifests itself in the representation using renormalized action bases. This also explains the reason why the staircase does not appear in the completely integrable system.