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The spectra of a microwave cylindrical resonator with the embedded thin metalrod playing the role of a singular perturbation are studied both theoreticallyand experimentally. The intra- and inter-mode scattering caused by theperturbation are clearly distinguished and recognized to play essentiallydifferent parts in the appearance of spectrum chaotic properties. The analysisbased on the mode-mixing operator norm shows that the inter-mode scatteringdominates over the intra-mode scattering and basically determines statisticalproperties of the resonator spectrum. The results we have obtained in theexperiment are in good conformity with our theory. Clear manifestations ofquantum chaos are revealed for the resonator with the asymmetrically insertedrod, namely, the Wigner-type distribution of the inter-frequency intervals, theapparent correlation between spectral lines, and the characteristic curve ofthe spectral rigidity. By comparing the theory and the experiment we succeededin establishing for the first time that it is just the inter-mode scatteringthat is responsible for the quantum chaos manifestations in the singularlyperturbed integrable wave-billiard system.

The mechanism of quantum chaos manifestations in the spectra of singularly perturbed wave-billiard systems