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

TL;DR

This paper investigates nonexponential energy dissipation in a lossy elastodynamic billiard, comparing experimental results with Porter-Thomas and random matrix theory predictions, revealing deviations and the effectiveness of supersymmetric models.

Contribution

It introduces a random matrix supersymmetric approach to accurately model dissipation behaviors across different coupling regimes in elastodynamic systems.

Findings

Experimental dissipation deviates from Porter-Thomas predictions at full coupling.

Random matrix supersymmetric calculations match observed data across all coupling strengths.

Nonexponential dissipation is confirmed in ultrasonic energy decay measurements.

Abstract

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.