Power spectrum analysis and missing level statistics of microwave graphs with violated time reversal invariance

TL;DR

This study experimentally analyzes microwave networks simulating chaotic quantum graphs with broken time reversal symmetry, demonstrating that spectral fluctuation measures effectively identify symmetries and missing levels in complex systems.

Contribution

It introduces a method combining power spectrum and spectral fluctuations to detect symmetries and missing levels in systems with violated time reversal invariance.

Findings

Power spectrum combined with spectral fluctuations identifies symmetries.

Method effectively detects missing levels in spectra.

Applicable to real physical systems like nuclei or molecules.

Abstract

We present experimental studies of the power spectrum and other fluctuation properties in the spectra of microwave networks simulating chaotic quantum graphs with violated time reversal in- variance. On the basis of our data sets we demonstrate that the power spectrum in combination with other long-range and also short-range spectral fluctuations provides a powerful tool for the identification of the symmetries and the determination of the fraction of missing levels. Such a pro- cedure is indispensable for the evaluation of the fluctuation properties in the spectra of real physical systems like, e.g., nuclei or molecules, where one has to deal with the problem of missing levels.