Direct regular-to-chaotic tunneling rates using the fictitious integrable system approach

TL;DR

This paper reviews a method using fictitious integrable systems to predict dynamical tunneling rates from regular to chaotic regions in mixed phase space systems, showing excellent agreement with numerical results.

Contribution

It introduces a fictitious integrable system approach specifically for direct regular-to-chaotic tunneling, applicable to quantum maps, billiards, and microcavities.

Findings

Excellent agreement with numerical tunneling rates

Applicable to quantum maps, billiards, and microcavities

Focuses on direct tunneling excluding nonlinear resonances

Abstract

We review the fictitious integrable system approach which predicts dynamical tunneling rates from regular states to the chaotic region in systems with a mixed phase space. It is based on the introduction of a fictitious integrable system that resembles the regular dynamics within the regular island. We focus on the direct regular-to-chaotic tunneling process which dominates, if nonlinear resonances within the regular island are not relevant. For quantum maps, billiard systems, and optical microcavities we find excellent agreement with numerical rates for all regular states.