Resonance-assisted tunneling in 4D normal-form Hamiltonians

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 expla...

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Bibliographic Details
Published in:arXiv.org 2019-04
Main Authors: Firmbach, Markus, Fritzsch, Felix, Ketzmerick, Roland, Bäcker, Arnd
Format: Article
Language:English
Subjects:
Mathematical models
Morphology
Qualitative analysis
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1901.02692