Statistics of resonances and time reversal reconstruction in aluminum acoustic chaotic cavities

Abstract

The statistical properties of wave propagation in classical chaotic systems are of fundamental interest in physics and are the basis for diagnostic tools in materials science. The statistical properties depend in particular also on the presence of time reversal invariance in the system, which can be verified independently by time reversal reconstruction experiments. As a model system to test the combination of statistical properties with the ability to perform time reversal reconstruction we investigated chaotic systems with time reversal invariance using ultrasonic waves in aluminum cavities. After excitation of the samples with a short acoustic pulse the reverberation responses were recorded and analyzed. In the analysis of the spectral density of the recorded responses we explicitly included the fact that not all resonances are detected. Reversibility of the excited wave dynamics in the cavity after a time delay was studied by reconstruction of the excitation pulse in time reversal experiments. The statistical properties of resonance frequencies in the cavities were obtained from the reverberant responses. The distribution of the transmission intensities displays random division of intensity between cavity waves in narrow frequency bands. The distribution of frequency spacing between neighboring cavity resonances and the spectral rigidity agree with the predictions for the Gaussian Orthogonal Ensemble. This agreement is achieved if a fraction of typically 25 percent of resonances is not detected in the experiment. The normalized amplitude of the pulse that is reconstructed in the time reversal experiments decays exponentially with the time delay between the original excitation pulse and the end of the reversed oscillation track. The exponential behavior exists for time delays longer than the inverse of the nearest neighbor resonance spacing.