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Quantum tunneling in ultra-near-integrable systems
Riku Iijima1, Ryonosuke Koda1, Yasutaka Hanada2
1Department of Physics, Tokyo Metropolitan University, Tokyo 192-0397, Japan.
Physical Review. E
|January 21, 2023
Summary
Quantum map eigenfunctions exhibit surprising step structures and nonmonotonic decay in their tunneling tails, even near integrable limits. This phenomenon arises from quantum resonance, leading to stretched exponential decay not typical in standard tunneling.
Area of Science:
- Quantum mechanics
- Classical dynamics
- Mathematical physics
Background:
- Studying the behavior of eigenfunctions in quantum systems is crucial for understanding quantum chaos.
- The tunneling tail of eigenfunctions provides insights into the transition between classical and quantum regimes.
- Integrable and near-integrable systems offer a baseline for comparison with more complex dynamics.
Purpose of the Study:
- To investigate the characteristics of the tunneling tail of eigenfunctions for quantum maps.
- To explore the emergence of nonmonotonic decay and step structures in these tails.
- To elucidate the underlying quantum mechanisms responsible for the observed phenomena.
Main Methods:
- Utilizing arbitrary precision arithmetic for high-accuracy numerical calculations.
- Employing an integrable basis derived from the Baker-Campbell-Hausdorff (BCH) formula.
- Analyzing the relationship between quantum resonance and the structure of tunneling tails.
Main Results:
- Observed nonmonotonic decaying tails with distinct step structures in quantum map eigenfunctions.
- Demonstrated that these structures appear even in systems very close to the integrable limit.
- Identified quantum resonance as the mechanism coupling eigenfunctions to excited states, causing the observed structure.
- Found that the step structure leads to a stretched exponential decay with respect to the inverse Planck constant.
Conclusions:
- The study reveals unexpected complexity in the tunneling tails of quantum map eigenfunctions.
- Quantum resonance plays a critical role in generating nonmonotonic decay and step structures.
- The observed stretched exponential decay deviates from typical tunneling behavior, highlighting unique quantum effects.
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