Experimental and numerical study of spectral properties of three-dimensional chaotic microwave cavities: The case of missing levels

TL;DR

This paper investigates the spectral properties of chaotic 3D microwave cavities with missing levels, revealing limitations of existing theories and proposing methods to estimate missing levels using random matrix theory.

Contribution

It provides an experimental and numerical analysis of missing-level statistics in chaotic microwave cavities, highlighting the inadequacy of current theories for unresolved resonances and suggesting alternative estimation methods.

Findings

Standard theoretical approaches fail for unresolved resonances.

Random matrix theory can estimate the fraction of missing levels.

Spectral statistics are significantly affected by unresolved resonances.

Abstract

We present an experimental and numerical study of missing-level statistics of chaotic three-dimensional microwave cavities. The nearest-neighbor spacing distribution, the spectral rigidity, and the power spectrum of level fluctuations were investigated. We show that the theoretical approach to a problem of incomplete spectra does not work well when the incompleteness of the spectra is caused by unresolved resonances. In such a case the fraction of missing levels can be evaluated by calculations based on random matrix theory.