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

TL;DR

This study combines theoretical analysis and experimental data to demonstrate that inter-mode scattering in a perturbed microwave resonator causes quantum chaos signatures, such as Wigner distributions and spectral correlations.

Contribution

It establishes for the first time that inter-mode scattering is the key mechanism behind quantum chaos in singularly perturbed wave-billiard systems.

Findings

Inter-mode scattering dominates intra-mode scattering.

Spectral properties match theoretical predictions.

Manifestations of quantum chaos are experimentally confirmed.

Abstract

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 intra- and inter-mode scattering caused by the perturbation are clearly distinguished and recognized to play essentially different parts in the appearance of spectrum chaotic properties. The analysis based on the mode-mixing operator norm shows that the inter-mode scattering dominates over the intra-mode scattering and basically determines statistical properties of the resonator spectrum. 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 for the first time that it is just the inter-mode scattering that is responsible for the quantum chaos manifestations in the singularly perturbed integrable wave-billiard system.