INTERMODE SCATTERING AS A SOURCE OF QUANTUM CHAOS IN A MICROWAVE RESONATOR SUBJECTED TO SINGULAR PERTURBATION

The spectra of a microwave cylindrical resonator with the embedded thin metal rod playing the role of a singular perturbation are studied both theoretically and experimentally. The intraand inter-mode scattering caused by the perturbation are clearly distinguished and recognized to play essentially different parts in the appearance of spectrum chaotic properties. Statistical analysis based on the mode-mixing operator norm shows that the singularity-induced intermode scattering results in the essential correlation of resonance frequencies. The results we have obtained in the experiment are in good conformity with our theory. Clear manifestations of quantum chaos are revealed for the resonator with the asymmetrically inserted rod, namely, the Wigner-type distribution of the inter-frequency intervals, the apparent correlation between spectral lines, and the characteristic curve of the spectral rigidity. By comparing the theory and the experiment we succeeded in establishing unequivocally and for the first time that it is just the inter-mode scattering that gives rise to quantum chaos in the spectrum of wave-billiard systems subjected to singular perturbation.