Coupled unidirectional chaotic microwave graphs

TL;DR

This study experimentally and numerically analyzes a coupled unidirectional chaotic microwave network, revealing spectral degeneracies and statistical properties that align with predictions from random matrix theory, despite the network's time-reversal symmetry.

Contribution

The paper introduces an experimental setup of coupled unidirectional microwave networks and compares spectral statistics with theoretical models, highlighting unexpected Gaussian unitary ensemble behavior.

Findings

Resonances are doubly degenerate within experimental resolution.

Spectral statistics and elastic enhancement factor resemble GUE predictions.

Doublet size distribution is close to Poisson distribution.

Abstract

We investigate experimentally the undirected open microwave network $\Gamma $ with internal absorption composed of two coupled directed halves, unidirectional networks $\Gamma_{+} $ and $\Gamma_{-} $, corresponding to two possible directions of motion on their edges. The two-port scattering matrix of the network $\Gamma$ is measured and the spectral statistics and the elastic enhancement factor of the network are evaluated. The comparison of the number of experimental resonances with the theoretical one predicted by the Weyl's law shows that within the experimental resolution the resonances are doubly degenerate. This conclusion was also corroborated by the numerical calculations. Though the network is characterized by the time reversal symmetry the missing level spectral statistics and the elastic enhancement factor are rather close to the Gaussian unitary ensemble predictions in random matrix theory. We used numerical calculations for the open non-dissipative quantum graph possessing the same structure as the microwave network $\Gamma$ to investigate the doublet structures in the spectrum which otherwise would not be experimentally resolved. We show that the doublet size distribution is close to the Poisson distribution.