Presentation of the Berry–Tabor conjecture in Lévy plates

Abstract

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 ( 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.