Resonance-assisted tunneling in 4D normal-form Hamiltonians
arXiv:1901.02692 · doi:10.1103/PhysRevE.99.042213
Abstract
Nonlinear resonances in the classical phase space lead to a significant enhancement of tunneling. We demonstrate that the double resonance gives rise to a complicated tunneling peak structure. Such double resonances occur in Hamiltonian systems with an at least four-dimensional phase space. To explain the tunneling peak structure, we use the universal description of single and double resonances by 4D normal-form Hamiltonians. By applying perturbative methods, we reveal the underlying mechanism of enhancement and suppression of tunneling and obtain excellent quantitative agreement. Using a minimal matrix, we obtain model an intuitive understanding.
arXiv comment14 pages, 8 figures
References in corpus (30)
- Mayavi: a package for 3D visualization of scientific data
- 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
- Intermolecular vibrational energy redistribution in DCO (X^2A'): Classical-Quantum correspondence, dynamical assignments of highly excited states, and phase space transport
- Regular-to-chaotic tunneling rates using a fictitious integrable system
- Visualization and comparison of classical structures and quantum states of 4D maps
- 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
- Chaos-assisted emission from asymmetric resonant cavity microlasers
- Resonance-assisted tunneling in three degrees of freedom without discrete symmetry
- Bifurcations of families of 1D-tori in 4D symplectic maps
- Perturbation-Free Prediction of Resonance-Assisted Tunneling in Mixed Regular--Chaotic Systems
- Dynamical tunneling in molecules: role of the classical resonances and chaos
- Complex paths for regular-to-chaotic tunneling rates
- Relevance of the resonance junctions on the Arnold web to dynamical tunneling and eigenstate delocalization
- Origin of the enhancement of tunneling probability in the nearly integrable system
- Fractional-Power-Law Level-Statistics due to Dynamical Tunneling
- Normal forms and complex periodic orbits in semiclassical expansions of Hamiltonian systems
- Complex-Path Prediction of Resonance-Assisted Tunneling in Mixed Systems
- Parametric perspective on highly excited states: case studies of CHBrClF and C2H2
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- Arnold web and dynamical tunneling in a four-site Bose-Hubbard model