Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime

TL;DR

This paper develops a unified theoretical framework to predict dynamical tunneling rates from regular to chaotic regions across quantum and semiclassical regimes, validated by numerical agreement.

Contribution

It combines direct tunneling and resonance-assisted mechanisms into a comprehensive model for tunneling rates.

Findings

Excellent agreement with numerical simulations.

Provides a qualitative method to identify relevant nonlinear resonances.

Bridges quantum and semiclassical tunneling theories.

Abstract

We derive a prediction of dynamical tunneling rates from regular to chaotic phase-space regions combining the direct regular-to-chaotic tunneling mechanism in the quantum regime with an improved resonance-assisted tunneling theory in the semiclassical regime. We give a qualitative recipe for identifying the relevance of nonlinear resonances in a given $\hbar$-regime. For systems with one or multiple dominant resonances we find excellent agreement to numerics.