Direct Regular-to-Chaotic Tunneling Rates Using the Fictitious Integrable System Approach

TL;DR

This paper reviews a method for calculating regular-to-chaotic tunneling rates in mixed phase space systems, applying it to kicked systems like the standard map and validating with numerical data.

Contribution

It introduces and applies the fictitious integrable system approach to determine tunneling rates, providing a practical tool for analyzing mixed phase space quantum systems.

Findings

Successful application to kicked systems including the standard map

Good agreement with numerical data

Provides a comprehensive overview of the method

Abstract

In systems with a mixed phase space, where regular and chaotic motion coexists, regular states are coupled to the chaotic region by dynamical tunneling. We give an overview on the determination of direct regular-to-chaotic tunneling rates using the fictitious integrable system approach. This approach is applied to different kicked systems, including the standard map, and successfully compared with numerical data. This text corresponds to Chapter 6 of the book: Dynamical Tunneling - Theory and Experiment, edited by S. Keshavamurthy and P. Schlagheck [Taylor and Francis CRC (2011)]. For a more extensive exposition see [Phys. Rev. E 82, 056208 (2010); arXiv:1009.0418v2].