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arXiv · 1901.02692

Resonance-assisted tunneling in 4D normal-form Hamiltonians

Markus Firmbach·Felix Fritzsch·Roland Ketzmerick·Arnd Bäcker
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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.

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Markus Firmbach, Felix Fritzsch, Roland Ketzmerick, Arnd Bäcker. 2019-04-24. Resonance-assisted tunneling in 4D normal-form Hamiltonians. https://doi.org/10.1103/physreve.99.042213

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