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Semiclassical reproducibility of sawtooth structure observed for a periodically perturbed rounded-rectangular
Kin'ya Takahashi1, Kensuke S Ikeda2
1Kyushu University, Research Institute for Information Technology, 744 Motooka Nishi-ku, Fukuoka 819-0395, Japan and AcsiomA Ltd, 3-8-33 Momochihama Sawara-ku, Fukuoka 814-0001, Japan.
Physical Review. E
|June 19, 2025
Summary
Tunneling probabilities in a periodically perturbed potential exhibit a sawtooth structure due to multi-quanta absorption. A semiclassical approach explains this phenomenon, revealing underlying mechanisms of quantum tunneling.
Area of Science:
- Quantum Mechanics
- Nonlinear Dynamics
- Condensed Matter Physics
Background:
- Previous work identified a sawtoothlike structure in tunneling probabilities for periodically perturbed potentials.
- This structure arises from multi-quanta absorption tunneling and exhibits sudden changes due to harmonic channel replacements.
Purpose of the Study:
- To explore the underlying semiclassical mechanism responsible for the sawtooth structure in tunneling probabilities.
- To analyze the role of complex branches and semiclassical methods in reproducing the observed tunneling behavior.
Main Methods:
- Application of semiclassical methods to analyze the sawtooth structure.
- Utilizing the Melnikov method to estimate the semiclassical weight and baseline of the tunneling probability.
- Analogy to Fourier decomposition using superposition of complex branches.
Main Results:
- The semiclassical method successfully reproduces the overall sawtooth structure, with deviations in narrow transition regions.
- The baseline of the sawtooth structure is accurately described by the Melnikov method.
- The average tunneling probability exhibits an exponential dependence on perturbation amplitude (ε).
Conclusions:
- Semiclassical analysis provides a robust framework for understanding the sawtooth tunneling phenomenon.
- The Melnikov method and superposition of complex branches are key to explaining the observed structure and its baseline.
- The study elucidates the intricate relationship between quantum tunneling, perturbation parameters, and semiclassical dynamics.
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