Instanton-noninstanton transition in nonintegrable tunneling processes: A renormalized perturbation approach

TL;DR

This paper introduces a renormalized perturbation theory to describe the instanton-noninstanton transition in quantum tunneling processes within nonintegrable systems, revealing common characteristics and mechanisms across different maps.

Contribution

It develops a new perturbation approach based on an integrable Hamiltonian to explain the I-NI transition in nonintegrable quantum maps, applicable to systems like the Hénon and standard maps.

Findings

The I-NI transition is characterized by a quenching of the renormalized transition matrix element.

Tunneling probability enhancement is due to a change in the tunneling mechanism.

The approach successfully explains the transition in different nonintegrable maps.

Abstract

The instanton-noninstanton (I-NI) transition in the tunneling process, which has been numerically observed in classically nonintegrable quantum maps, can be described by a perturbation theory based on an integrable Hamiltonian renormalized so as to incorporate the integrable part of the map. The renormalized perturbation theory is successfully applied to the two quantum maps, the H\'enon and standard maps. In spite of different nature of tunneling in the two systems, the I-NI transition exhibits very common characteristics. In particular, the manifestation of I-NI transition is obviously explained by a remarkable quenching of the renormalized transition matrix element. The enhancement of tunneling probability after the transition can be understood as a sudden change of the tunneling mechanism from the instanton to quite a different mechanism supported by classical flows just outside of the stable-unstable manifolds of the saddle on the top of the potential barrier.