Complex paths for regular-to-chaotic tunnelling rates

2012/07/04 by N. Mertig, Normann Mertig, S. Löck +7 · 1 citation
Physics and Astronomy · #Chaotic #Hamiltonian (control theory) #Hamiltonian system #Motion (physics) #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos #Quantum chaos and dynamical systems #Quantum many-body systems #Quantum tunnelling #Standard map #Torus #nlin.CD #quant-ph

paper · pdf · doi:10.1209/0295-5075/102/10005

5 pages, 4 figures

arxiv created 2012/07/04 · openalex publication_date 2013/04/01 · arxiv updated 2015/06/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations

• Flooding of Chaotic Eigenstates into Regular Phase Space Islands
• Chaos-Assisted Directional Light Emission from Microcavity Lasers
• Julia set describes quantum tunnelling in the presence of chaos
• First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard
• Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime
• Universality in the flooding of regular islands by chaotic states
• Semiclassical approximations in wave mechanics
• Dynamical Tunneling in Mushroom Billiards
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• Eigenstates Ignoring Regular and Chaotic Phase-Space Structures
• Semiclassical Description of Tunneling in Mixed Systems: Case of the Annular Billiard
• Chaos-assisted tunneling with cold atoms
• A universal instability of many-dimensional oscillator systems

Cited by

• Chaos and Quantum Tunneling