Complex paths for regular-to-chaotic tunneling rates

TL;DR

This paper introduces a semiclassical complex path method to predict dynamical tunneling rates from regular to chaotic regions in Hamiltonian systems, validated by the standard map with high accuracy.

Contribution

The paper presents a novel semiclassical complex path approach for calculating dynamical tunneling rates in Hamiltonian systems, improving predictive accuracy.

Findings

Excellent agreement with numerical tunneling rates for the standard map

Validates the semiclassical complex path approach for dynamical tunneling

Provides a new tool for analyzing quantum-classical correspondence in chaotic systems

Abstract

In generic Hamiltonian systems tori of regular motion are dynamically separated from regions of chaotic motion in phase space. Quantum mechanically these phase-space regions are coupled by dynamical tunneling. We introduce a semiclassical approach based on complex paths for the prediction of dynamical tunneling rates from regular tori to the chaotic region. This approach is demonstrated for the standard map giving excellent agreement with numerically determined tunneling rates.