ASA 125th Meeting Ottawa 1993 May

4pSA5. Quantum chaos methods applied to high-frequency plate vibrations.

O. Legr

Lab. de Phys. de la Matiere Condensee, CNRS URA 190, Faculte des Sci., Parc Valrose, B.P. 70, 06108 Nice Cedex 02, France

X-RS, Parc-Club, 91893 Orsay, France

C. Schmit

Div. of Phys. Theor., IPN, Orsay, France

X-RS, Parc-Club, Orsay, France

D. Sornette

Lab. de Phys. de la Metiere Consensee, CNRS URA 190, Nice, France

X-RS Parc-Club, Orsay, France

The first investigation of the quasiclassical regime of thin plate vibrations in the high-frequency regime is presented. Using an efficient numerical scheme to compute many eigenfrequencies of a stadium-shaped plate, it is found that the distribution of level spacings and the spectrum rigidity follow the GOE (Gaussian orthogonal ensemble) random matrix statistics. An asymptotic equivalence between the spectrum of a clamped plate and that of a membrane with a mixed boundary condition is derived. Also, examples of eigenmodes that present scars are present, and their quantization is given. [This work has been published in Europhys. Lett. 18, 101--106 (1992).]