Spectra and spectral correlations of microwave graphs with symplectic symmetry

TL;DR

This paper reports on the experimental realization of microwave graphs with symplectic symmetry, confirming theoretical predictions about spectral statistics and symmetry breaking effects in such systems.

Contribution

It demonstrates the first experimental implementation of microwave graphs with antiunitary symmetry T satisfying T^2=-1 and analyzes their spectral properties.

Findings

Spectral level spacings match Gaussian symplectic ensemble predictions.

Kramers doublets are clearly identified and can be lifted by symmetry-breaking perturbations.

Transition from GSE to GOE statistics observed by tuning symmetry.

Abstract

Following an idea by Joyner et al. [EPL, 107 (2014) 50004] a microwave graph with antiunitary symmetry T obeying T^2=-1 has been realized. The Kramers doublets expected for such systems have been clearly identified and could be lifted by a perturbation which breaks the antiunitary symmetry. The observed spectral level spacings distribution of the Kramers doublets is in agreement with the predictions from the Gaussian symplectic ensemble (GSE), expected for chaotic systems with such a symmetry. In addition results on the two-point correlation function, the spectral form factor, the number variance and the spectral rigidity are presented, as well as on the transition from GSE to GOE statistics by continuously changing T from T^2=-1 to T^2=1.