| ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS |
Prev
Next
|
|
|
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 |
|
|
|
|
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.
|
Received: 10 October 2023
Revised: 14 December 2023
Accepted manuscript online: 24 January 2024
|
|
PACS:
|
42.50.Lc
|
(Quantum fluctuations, quantum noise, and quantum jumps)
|
| |
47.10.Df
|
(Hamiltonian formulations)
|
| |
33.20.Tp
|
(Vibrational analysis)
|
|
| 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
|
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
|
[1] Brody T A, Flores J, French J B, Mello P A, Pandey A and Wong S S M 1981 Rev. Mod. Phys. 53 385
[2] Müller S, Heusler S, Altland A, Braun P and Haake F 2009 New J. Phys. 11 103025
[3] Porter C E 1965 Fluctuations of Quantal Spectra (New York: Academic Press) p. 8
[4] Berry M V, Tabor and Ziman J M 1977 Proc. R. Soc. 356 375
[5] Casati G, Chirikov B V and Guarneri I 1985 Phys. Rev. Lett. 54 1350
[6] Bohigas O, Giannoni M J and Schmit C 1984 Phys. Rev. Lett. 52 1
[7] Mehta M L 1990 Random Matrix Theory, 3rd Edn. (New York: Springer) p. 13
[8] Stöckmann H J and Stein J 1990 Phys. Rev. Lett. 64 2215
[9] Frank O and Eckhardt B 1996 Phys. Rev. E 53 4166
[10] Mohammadesmaeili R, Motaghian S and Mofid M 2021 Eur. J. Mech. A Solids 88 104274
[11] Nguyen P, Pham Q H, Tran T T and Nguyen T 2022 Ain Shams Eng. J. 13 101615
[12] Warburton G B and Edney S L 1984 J. Sound Vib. 95 537
[13] Leissa A 1969 Vibration of Plates (NASA: Scientific and Technical Information Division)
[14] Biancolini M E, Brutti C and Reccia l 2005 J. Sound Vib. 288 321
[15] Ellegaard C, Guhr T, Lindemann K, Lorensen H Q, Nygard J and Oxborrow M 1995 Phys. Rev. Lett. 75 1546
[16] Bertelsen P, Ellegaard C and Hugues E 2000 Eur. Phys. J. B 15 18
[17] Andersen A, Ellegaard C, Jackson A D and Schaadt K 2001 Phys. Rev. E 63 066204
[18] Sondergaard, Niels and Tanner Gregor 2002 Phys. Rev. E 66 066211
[19] Gregor Tanner and Niels Søndergaard 2007 J. Phys. A: Math. Theor. 40 R443
[20] López-González J L, Franco-Villafañe J A, Méndez-Sánchez R A, Zavala-Vivar G, Flores-Olmedo E, Arreola-Lucas A and Báez G 2021 Phys. Rev. E 103 043004
[21] Timoshenko SP and Woinowsky-Krieger SW 1959 Theory of plates and shells (New York: McGraw-Hill) p. 180
[22] Reddy J N 2007 Theory and Analysis of Elastic plates and Shells, 2nd Edn. (New York: CRC Press) p. 331
[23] Hetenyi Miklos 1946 Beams on Elastic Foundation: Theory with Applications in the Fields of Civil and Mechanical Engineering (Ann Arbor: University of Michigan Press) p. 179
[24] Qiao Y F, Hou G L and Chen A 2021 Appl. Math. Model. 89 1124
[25] Qiao Y F, Hou G L and Chen A 2021 Appl. Math. Comput. 400 126043
[26] Sun Z Q, Hou G L, Qiao Y F and Liu J C 2023 Chin. Phys. B 33 016107
[27] Yao W A, Zhong W X and Lim C W 2009 Symplectic Elasticity (Singapore: World Scientific) p. 71
[28] Zhong Y, Li R, Liu Y M and Tian B 2009 Int. J. Solids Struct. 46 2506
[29] Su X, Bai E and Chen A 2021 Int. J. Struct. Stab. Dyn. 21 2150122
[30] Su X and Bai E 2022 J. Vib. Control. 28 3
[31] Leissa A W 1973 J. Sound Vib. 31 257
[32] Omurtag M H and Kadıolu F 1998 Comput. Struct. 67 253
[33] Matsushita T and Terasaka T 1984 Chem. Phys. Lett. 105 511
[34] Richens P J and Berry M V 1981 Physica D 2 495
[35] Robnik M 1987 J. Phys. A: Math. Gen. 20 L495
[36] Dietz B and Haake F 1990 Z. Phys. B 80 153
[37] Pechukas P 1983 Phys. Rev. Lett. 51 943
[38] Oganesyan V and David A H 2007 Phys. Rev. B 75 155111
[39] Atas Y Y, Bogomolny E, Giraud O and Roux G 2013 Phys. Rev. Lett. 110 084101
[40] Atas Y Y, Bogomolny E, Giraud O and Roux G 2013 J. Phys. A: Math. Theor. 46 355204
[41] Bogomolny E and Hugues E 1998 Phys. Rev. E 57 5404 |
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
