# Missing level statistics and the power spectrum of level fluctuations analysis of three-dimensional chaotic microwave cavities

## TL;DR

This paper experimentally investigates missing level statistics and the power spectrum of level fluctuations in three-dimensional chaotic microwave cavities, demonstrating methods to determine the fraction of missing levels using spectral analysis.

## Contribution

It introduces a combined spectral analysis approach to accurately identify the fraction of missing levels in wave-chaotic systems, validated by experimental data.

## Key findings

- Power spectrum analysis effectively estimates missing levels.
- Analytical models match experimental data for incomplete spectra.
- RMT calculations assist when unresolved states are numerous.

## Abstract

We present an experimental study of missing level statistics of three-dimensional chaotic microwave cavities. The investigation is reinforced by the power spectrum of level fluctuations analysis which also takes into account the missing levels. On the basis of our data sets we demonstrate that the power spectrum of level fluctuations in combination with short- and long-range spectral fluctuations provides a powerful tool for the determination of the fraction of randomly missing levels in systems that display wave chaos such as the three-dimensional chaotic microwave cavities. The experimental results are in good agreement with the analytical expressions that explicitly take into account the fraction of observed levels. We also show that in the case of incomplete spectra with many unresolved states the above procedures may fail. In such a case the random matrix theory calculations can be useful for the determination of missing levels.