QUANTUM CHAOS METHODS APPLIED TO HIGH-FREQUENCY PLATE VIBRATIONS

The first investigation of the quasi-classical 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, we find 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. We also present examples of eigenmodes which present scars and give their quantization.