Long-range correlations in rectangular cavities containing point-like perturbations

TL;DR

This study experimentally examines the spectral correlations in rectangular microwave cavities with point-like perturbations, revealing a transition to semi-Poisson statistics at higher frequencies and validating a theoretical model for such systems.

Contribution

It extends previous work by analyzing long-range spectral correlations and power spectra, confirming the semi-Poisson transition in perturbed billiards.

Findings

Spectral properties shift to semi-Poisson with increasing frequency

Long-range correlations match theoretical predictions

Experimental data aligns with a zero-range perturbation model

Abstract

We investigated experimentally the short- and long-range correlations in the fluctuations of the resonance frequencies of flat, rectangular microwave cavities that contained antennas acting as point-like perturbations. We demonstrate that their spectral properties exhibit the features typical for singular statistics. Hitherto, only the nearest-neighbor spacing distribution had been studied. We, in addition considered statistical measures for the long-range correlations and analyzed power spectra. Thereby, we could corroborate that the spectral properties change to semi-Poisson statistic with increasing microwave frequency. Furthermore, the experimental results are shown to be well described by a model applicable to billiards containing a zero-range perturbation [T. Tudorovskiy et al., New. J. Phys. 12, 12302 (2010)].