A microwave realization of the Gaussian symplectic ensemble

TL;DR

This paper demonstrates a microwave graph system that exhibits Gaussian symplectic ensemble statistics, confirming theoretical predictions for systems with antiunitary symmetry T satisfying T^2=-1, and explores symmetry breaking effects.

Contribution

It provides the first microwave realization of the Gaussian symplectic ensemble with clear identification of Kramers doublets and their perturbation-induced lifting.

Findings

Spectral level spacings match Gaussian symplectic ensemble predictions

Kramers doublets are clearly identified in the microwave graph

Symmetry breaking perturbation lifts the doublets as expected

Abstract

Following an idea by Joyner et al. [Europhys. Lett. 107, 50004 (2014)] a microwave graph with an antiunitary symmetry T obeying T^2=-1 is realized. The Kramers doublets expected for such systems are clearly identified and can 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 expected for chaotic systems with such a symmetry.