Perturbation-Free Prediction of Resonance-Assisted Tunneling in Mixed Regular--Chaotic Systems
arXiv:1607.06477 · doi:10.1103/PhysRevE.94.062220
Abstract
For generic Hamiltonian systems we derive predictions for dynamical tunneling from regular to chaotic phase-space regions. In contrast to previous approaches, we account for the resonance-assisted enhancement of regular-to-chaotic tunneling in a non-perturbative way. This provides the foundation for future semiclassical complex-path evaluations of resonance-assisted regular-to-chaotic tunneling. Our approach is based on a new class of integrable approximations which mimic the regular phase-space region and its dominant nonlinear resonance chain in a mixed regular--chaotic system. We illustrate the method for the standard map.
arXiv comment20 pages, 11 figures
References in corpus (28)
- Non-dispersive wave packets in periodically driven quantum systems
- First Experimental Evidence for Chaos-Assisted Tunneling in a Microwave Annular Billiard
- Chaos-assisted directional light emission from microcavity lasers
- Resonance-assisted tunneling in near-integrable systems
- Resonance-Assisted Tunneling
- Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime
- Dynamical tunneling in mushroom billiards
- Resonance- and chaos-assisted tunneling in mixed regular-chaotic systems
- Regular-to-chaotic tunneling rates using a fictitious integrable system
- Ionization via Chaos Assisted Tunneling
- Dynamical tunneling in molecules: Quantum routes to energy flow
- Quality factors and dynamical tunneling in annular microcavities
- Direct regular-to-chaotic tunneling rates using the fictitious integrable system approach
- Decay of Quantum Accelerator Modes
- Experimental Observation of Resonance-Assisted Tunneling
- Observation of resonance-assisted dynamical tunneling in an asymmetric microcavity
- On dynamical tunneling and classical resonances
- Instantons revisited: dynamical tunnelling and resonant tunnelling
- Chaos-assisted emission from asymmetric resonant cavity microlasers
- The Poincare-Birkhoff theorem in Quantum Mechanics
- Dynamical tunneling in molecules: role of the classical resonances and chaos
- Resonance-assisted decay of nondispersive wave packets
- Complex paths for regular-to-chaotic tunneling rates
- Origin of the enhancement of tunneling probability in the nearly integrable system
- Semiclassical description of resonance-assisted tunneling in one-dimensional integrable models
- Integrable Approximation of Regular Islands: The Iterative Canonical Transformation Method
- Integrable approximation of regular regions with a nonlinear resonance chain
- Universal wave functions structure in mixed systems
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- Resonance spectra for quantum maps of kicked scattering systems by complex scaling
- Dynamical tunneling across the separatrix