Nonexponential dissipation in a lossy elastodynamic billiard: comparison with Porter-Thomas and random matrix...

Area of Science:

• Mesoscopic physics
• Quantum chaos
• Acoustic metamaterials

Background:

• Understanding energy dissipation is crucial in mesoscopic systems.
• Quantum dots serve as analogs for studying fundamental physical phenomena.
• Ultrasonic energy dissipation in reverberant bodies coupled to waveguides is not fully understood.

Purpose of the Study:

• To investigate the dissipation of diffuse ultrasonic energy in a reverberant body coupled to a waveguide.
• To compare experimental measurements with theoretical predictions, including the Porter-Thomas distribution.
• To explore deviations from simple models, particularly in cases of fully open channels.

Main Methods:

• Experimental setup involving a reverberant body coupled to a waveguide.
• Measurement of ultrasonic energy dissipation.
• Comparison with a simple theoretical model predicting Porter-Thomas distribution.
• Application of random matrix supersymmetric calculations.

Main Results:

• Experimental confirmation of nonexponential dissipation predicted by the simple model for most cases.
• Statistically significant deviations observed for fully open channels.
• Accurate modeling of all observed behaviors across coupling strengths using random matrix supersymmetric calculations.

Conclusions:

• The study validates a simple model for ultrasonic energy dissipation in certain mesoscopic analogs.
• Deviations in fully open channels highlight the limitations of basic models.
• Random matrix supersymmetric theory provides a robust framework for describing dissipation in these systems.