Presentation of the Berry-Tabor conjecture in Levy plates  

作　　者：Chao Li Guo-Lin Hou 李超;侯国林(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China)

机构地区：[1]School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China

出　　处：《Chinese Physics B》2024年第10期240-247,共8页中国物理B（英文版）

基　　金：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);the Innovation Program for Graduate Education of Inner Mongolia University(Grant No.11200-5223737).

摘　　要：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(r),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(r)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.

关 键 词：Berry-Tabor conjecture frequency spectra Hamiltonian approach Lévy plates 

分 类 号：O413[理学—理论物理]