# Non-universality in the spectral properties of time-reversal invariant microwave networks and quantum graphs

## TL;DR

This study shows that quantum graphs with time-reversal symmetry exhibit universal short-range spectral fluctuations but deviate in long-range fluctuations due to short periodic orbits, challenging their ideal use in quantum chaos research.

## Contribution

The paper demonstrates the non-universality of long-range spectral fluctuations in time-reversal invariant quantum graphs through experimental and numerical analysis.

## Key findings

- Short-range spectral fluctuations align with random matrix theory.
- Long-range fluctuations deviate due to short periodic orbits.
- Length spectra analysis supports the deviation explanation.

## Abstract

We present experimental and numerical results for the long-range fluctuation properties in the spectra of quantum graphs with chaotic classical dynamics and preserved time-reversal invariance. Such systems are generally believed to provide an ideal basis for the experimental study of prob- lems originating from the field of quantum chaos and random matrix theory. Our objective is to demonstrate that this is true only for short-range fluctuation properties in the spectra, whereas the observation of deviations in the long-range fluctuations is typical for quantum graphs. This may be attributed to the unavoidable occurrence of short periodic orbits, which explore only the individual bonds forming a graph and thus do not sense the chaoticity of its dynamics. In order to corrobo- rate our supposition, we performed numerous experimental and corresponding numerical studies of long-range fluctuations in terms of the number variance and the power spectrum. Furthermore, we evaluated length spectra and compared them to semiclassical ones obtained from the exact trace formula for quantum graphs.