Non-exponential Dissipation in a Lossy Elastodynamic Billiard, Comparison with Porter-Thomas and Random Matrix Predictions

We study the dissipation of diffuse ultrasonic energy in a reverberant body coupled to a waveguide, an analog for a mesoscopic electron in a quantum dot. A simple model predicts a Porter-Thomas like distribution of level widths and corresponding nonexponential dissipation, a behavior largely confirmed by measurements. For the case of fully open channels, however, measurements deviate from this model to a statistically significant degree. A random matrix supersymmetric calculation is found to accurately model the observed behaviors at all coupling strengths.