Perturbation-Free Prediction of Resonance-Assisted Tunneling in Mixed Regular--Chaotic Systems

TL;DR

This paper introduces a non-perturbative method to predict resonance-assisted tunneling in mixed regular-chaotic systems, using integrable approximations to model phase-space regions and resonances, exemplified on the standard map.

Contribution

It presents a novel, perturbation-free approach for predicting resonance-assisted tunneling in Hamiltonian systems, improving upon previous methods.

Findings

Accurate predictions for dynamical tunneling in mixed systems.

New integrable approximations effectively model phase-space resonances.

Method demonstrated successfully on the standard map.

Abstract

For generic Hamiltonian systems we derive predictions for dynamical tunneling from regular to chaotic phase-space regions. In contrast to previous approaches, we account for the resonance-assisted enhancement of regular-to-chaotic tunneling in a non-perturbative way. This provides the foundation for future semiclassical complex-path evaluations of resonance-assisted regular-to-chaotic tunneling. Our approach is based on a new class of integrable approximations which mimic the regular phase-space region and its dominant nonlinear resonance chain in a mixed regular--chaotic system. We illustrate the method for the standard map.