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Presentation of the Berry-Tabor conjecture in Lévy plates |
| Chao Li(李超) and Guo-Lin Hou(侯国林)† |
| School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China |
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Abstract The Berry-Tabor (BT) conjecture is a famous statistical inference in quantum chaos, which not only establishes the spectral fluctuations of quantum systems whose classical counterparts are integrable but can also be used to describe other wave phenomena. In this paper, the BT conjecture has been extended to Lévy plates. As predicted by the BT conjecture, level clustering is present in the spectra of Lévy plates. The consequence of level clustering is studied by introducing the distribution of nearest neighbor frequency level spacing ratios $P\left( {\widetilde r} \right)$, which is calculated through the analytical solution obtained by the Hamiltonian approach. Our work investigates the impact of varying foundation parameters, rotary inertia, and boundary conditions on the frequency spectra, and we find that $P\left({\widetilde r} \right)$ conforms to a Poisson distribution in all cases. The reason for the occurrence of the Poisson distribution in the Lévy plates is the independence between modal frequencies, which can be understood through mode functions.
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Received: 10 October 2023
Revised: 14 December 2023
Accepted manuscript online: 24 January 2024
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PACS:
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42.50.Lc
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(Quantum fluctuations, quantum noise, and quantum jumps)
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47.10.Df
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(Hamiltonian formulations)
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33.20.Tp
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(Vibrational analysis)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12261064 and 11861048), the Natural Science Foundation of Inner Mongolia, China (Grant No. 2021MS01004), and the Innovation Program for Graduate Education of Inner Mongolia University (Grant No. 11200-5223737). |
Corresponding Authors:
Guo-Lin Hou
E-mail: smshgl@imu.edu.cn
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Cite this article:
Chao Li(李超) and Guo-Lin Hou(侯国林) Presentation of the Berry-Tabor conjecture in Lévy plates 2024 Chin. Phys. B 33 104204
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