No abstract

We measure the amplitude of the elastomechanical displacement at a fine grid of points on a free plate having the shape of a Sinai stadium. The obtained displacement field formally corresponds to a wave function in a quantum system. While the distribution of the squared amplitudes agrees with the prediction of random matrix theory (RMT), there is a strong deviation of the spatial correlator from the standard prediction for quantum chaotic systems. We show that this is due to the presence of two modes, leading to a beating phenomenon. We construct a proper extension of the spatial correlator within the framework of RMT.

The parametric variation of the eigenfrequencies of a chaotic plate is measured and compared to random matrix theory using recently calculated universal correlation functions. The sensitivity of the flexural modes of the plate to pressure is used to isolate this symmetry class of modes and simplify the data analysis. The size of the plate is used as the external parameter and the eigenvalues are observed to undergo one or two oscillations in the experimental window. The correlations of the eigenvalues are in good agreement with statistical measures such as the parametric number variance, the velocity autocorrelation, and the intralevel velocity autocorrelation derived for the Gaussian orthogonal ensemble of random matrix theory. Our results show that the theory can be also applied to wave systems other than quantum systems.

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.

We present experimental results for the ultrasound transmission spectra and standing wave patterns of a rectangular block of fused quartz. A comparison is made between our data and an approximation of the theoretical staircase function for three-dimensional isotropic elasticity. The main emphasis of our study is on the role of mode conversion in regular ray-splitting billiards. We present the fluctuation statistics and find that these are described by the Gaussian orthogonal ensemble of random matrix theory, despite the fact that the system is not classically chaotic, as demonstrated with numerical simulation. Using temperature perturbation, we find that the vast majority of the resonances are mixtures of transverse and longitudinal wave motion, yet a small number of special resonances remain pure. We further illuminate this by presenting standing wave patterns measured on one face of the block.