Nonuniversal Deviations From Predictions of the Random Matrix Theory of Wave Chaotic Scattering: Theory and Experiment

The eigenfunctions and spectra of chaotic billiards are notoriously sensitive to small perturbations.~ Thus statistical approaches have been developed to model such systems.~ In recent work, we used random matrix theory to develop statistical models for the impedance of a chaotic microwave cavity coupled to a small number of antennas, with the only parameters being the radiation impedance of the antennas, the area of the cavity and a uniform loss parameter Q [S. Hemmady, \textit{et al.}, Phys. Rev. Lett. \textbf{94}, 014102 (2005); X. Zheng, \textit{et al}., Electromagnetics \textbf{26}, 3 (2006)].~ The theory generally agrees well with experiment, but under some circumstances the experimental and numerical results deviate significantly from the Random Matrix Theory predictions.~ We have derived a method of accounting for these deviations and have experimental and numerical results which agree well with our new, non-universal, predictions.