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

2010/09/30 by Arnd Bäcker, Roland Ketzmerick, Steffen Löck · 3 citations
Computer Science · Physics and Astronomy · #Chaotic #Classical mechanics #Computer science #Dynamical billiards #Focus (optics) #Integrable system #Mathematical physics #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Nonlinear system #Optics #Phase space #Physics #Quantum #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum mechanics #Quantum tunnelling #Space (punctuation) #Standard map #Statistical physics #nlin.CD #quant-ph

paper · pdf · doi:10.1103/physreve.82.056208

published as Phys. Rev. E 82, 056208 (2010) · 26 pages, 24 figures

openalex publication_date 2010/11/19 · arxiv created 2010/11/22 · arxiv updated 2010/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Level spacing distribution in systems with partially chaotic classical dynamics
• Flooding of Chaotic Eigenstates into Regular Phase Space Islands
• Chaos-Assisted Directional Light Emission from Microcavity Lasers
• First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard
• Classical and Quantum Hamiltonian Ratchets
• Nanowires with surface disorder: Giant localization length and dynamical tunneling in the presence of directed chaos
• Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime
• Universality in the flooding of regular islands by chaotic states
• Quantum-to-Classical Crossover of Quasibound States in Open Quantum Systems
• Dynamical tunneling in mixed systems
• Influence of classical resonances on chaotic tunneling
• Dynamical Tunneling in Mushroom Billiards
• Quantum mushroom billiards
• On dynamical tunneling and classical resonances
• Regular-to-Chaotic Tunneling Rates Using a Fictitious Integrable System
• Eigenstates Ignoring Regular and Chaotic Phase-Space Structures
• Recovery of chaotic tunneling due to destruction of dynamical localization by external noise
• Semiclassical Description of Tunneling in Mixed Systems: Case of the Annular Billiard
• Stickiness in mushroom billiards
• A universal instability of many-dimensional oscillator systems

Cited by

• Direct Regular-to-Chaotic Tunneling Rates Using the Fictitious Integrable System Approach
• Chaos and Quantum Tunneling
• Instanton-noninstanton transition in nonintegrable tunneling processes: A renormalized perturbation approach