Complex paths for regular-to-chaotic tunneling rates

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.

5 pages, 4 figures

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• Quantum Goos-Hänchen shift and tunneling transmission at a curved step potential
• Perturbation-Free Prediction of Resonance-Assisted Tunneling in Mixed Regular--Chaotic Systems
• Chaos-Assisted Long-Range Tunneling for Quantum Simulation
• Semiclassical description of resonance-assisted tunneling in one-dimensional integrable models
• Complex-Path Prediction of Resonance-Assisted Tunneling in Mixed Systems
• Integrable Approximation of Regular Islands: The Iterative Canonical Transformation Method
• Resonance-assisted tunneling in 4D normal-form Hamiltonians
• Integrable approximation of regular regions with a nonlinear resonance chain
• Dynamical tunneling across the separatrix
• Temporal flooding of regular islands by chaotic wave packets