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.
14 pages, 8 figures
References in corpus (12)
- Mayavi: a package for 3D visualization of scientific data
- Chaos-assisted directional light emission from microcavity lasers
- Dynamical tunneling in mushroom billiards
- Regular-to-chaotic tunneling rates using a fictitious integrable system
- Quality factors and dynamical tunneling in annular microcavities
- Direct regular-to-chaotic tunneling rates using the fictitious integrable system approach
- On dynamical tunneling and classical resonances
- Chaos-assisted emission from asymmetric resonant cavity microlasers
- Perturbation-Free Prediction of Resonance-Assisted Tunneling in Mixed Regular--Chaotic Systems
- Fractional-Power-Law Level-Statistics due to Dynamical Tunneling
- Origin of the enhancement of tunneling probability in the nearly integrable system
- Complex-Path Prediction of Resonance-Assisted Tunneling in Mixed Systems