Distribution of resonance strengths in microwave billiards of mixed and chaotic dynamics

Abstract

A new measure for statistical properties of the wave function components of quantum systems, the distribution of the product of two partial widths, is introduced. It is tested with data obtained in analog experiments with microwave billiards, where the product of two partial widths equals the resonance strengths in the microwave spectra. The billiards are from the family of the Limaçons, one with chaotic and two with mixed classical dynamics. For completely chaotic systems the partial widths generically obey a Porter-Thomas distribution. We show that in this case the distribution of their product equals a K0 distribution. While we find deviations of the experimental strength distribution from the K0 distribution for the billiards with mixed dynamics, the distributions agree perfectly for the chaotic billiard, when taking into account the experimental threshold of detection in the theoretical description. Hence, the strength distribution provides another stringent test for the connection between statistical properties of systems with classical chaotic dynamics and random matrix theory.