Regular-to-chaotic tunneling rates using a fictitious integrable system

TL;DR

This paper introduces a formula to predict dynamical tunneling rates from regular to chaotic regions in mixed phase space systems, using a fictitious integrable system approach, validated by numerical results.

Contribution

The paper presents a novel method employing a fictitious integrable system to accurately predict tunneling rates in mixed phase space systems.

Findings

Agreement with numerical results for standard map

Effective in regimes without resonance-assisted tunneling

Applicable to various kicked systems

Abstract

We derive a formula predicting dynamical tunneling rates from regular states to the chaotic sea in systems with a mixed phase space. Our approach is based on the introduction of a fictitious integrable system that resembles the regular dynamics within the island. For the standard map and other kicked systems we find agreement with numerical results for all regular states in a regime where resonance-assisted tunneling is not relevant.