Gaussian Orthogonal Ensemble Statistics in a Microwave Stadium Billiard with Chaotic Dynamics: Porter-Thomas Distribution and Algebraic Decay of Time Correlations

Abstract

The complete set of resonance parameters for 950 resonances of a superconducting microwave cavity connected to three antennas has been measured. This cavity simulates the quantum mechanics of a particle in a Bunimovich stadium. The partial widths are found to follow a Porter-Thomas distribution. The Fourier transforms of the $S$-matrix autocorrelation functions decay algebraically (nonexponentially) in time. These results agree perfectly with the predictions of random-matrix theory. They constitute one of the most stringent tests ever of this expected connection between chaotic dynamics and randommatrix theory.