Random matrix theory and acoustic resonances in plates with an approximate symmetry

A. Andersen, C. Ellegaard, A. D. Jackson, and K. Schaadt
Phys. Rev. E 63, 066204 – Published 15 May 2001
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Abstract

We discuss a random matrix model of systems with an approximate symmetry and present the spectral fluctuation statistics and eigenvector characteristics for the model. An acoustic resonator like, e.g., an aluminum plate may have an approximate symmetry. We have measured the frequency spectrum and the widths for acoustic resonances in thin aluminum plates, cut in the shape of the so-called three-leaf clover. Due to the mirror symmetry through the middle plane of the plate, each resonance of the plate belongs to one of two mode classes and we show how to separate the modes into these two classes using their measured widths. We compare the spectral statistics of each mode class with results for the Gaussian orthogonal ensemble. By cutting a slit of increasing depth on one face of the plate, we gradually break the mirror symmetry and study the transition that takes place as the two classes are mixed. Presenting the spectral fluctuation statistics and the distribution of widths for the resonances, we find that this transition is well described by the random matrix model.

  • Received 30 November 2000

DOI:https://doi.org/10.1103/PhysRevE.63.066204

©2001 American Physical Society

Authors & Affiliations

A. Andersen1, C. Ellegaard2, A. D. Jackson2, and K. Schaadt2

  • 1Department of Physics, The Technical University of Denmark, DK-2800 Lyngby, DenmarkRisø National Laboratory, Optics and Fluid Dynamics Department, DK-4000 Roskilde, Denmark
  • 2The Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark

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Vol. 63, Iss. 6 — June 2001

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