Spectra and spectral correlations of microwave graphs with symplectic symmetry

Abstract

Following an idea by Joyner et al. [Europhys. Lett. 107, 50004 (2014)EULEEJ0295-507510.1209/0295-5075/107/50004], a microwave graph with antiunitary symmetry T obeying T^{2}=-1 has been realized, thus mimicking a spin-1/2 system. 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-spacing distribution of the Kramers doublets agreed with the predictions from the Gaussian symplectic ensemble (GSE), expected for chaotic systems with such a symmetry. In addition, we studied the random matrix equivalents of the used graphs both analytically and numerically. Here small deviations from the GSE level-spacing distribution were found, too small to be seen in the experiment but clearly visible in the simulations. Furthermore, 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 Gaussian symplectic to Gaussian orthogonal statistics by continuously changing T from T^{2}=-1 to T^{2}=1.

Microwave Studies of Three Chiral Ensembles in Chains of Coupled Dielectric Resonators

“…Like (25) in the main text, these results are valid for the specific value of N they were derived for. This is due to the fact that the matrices A are sparse for N > 3.…”

“…In a recent paper we succeeded in the realization of the Gaussian symplectic ensemble in a microwave graph mimicking a spin 1/2 system [25]. The main ingredients had been two subgraphs, complex conjugate to each other, coupled by a pair of bonds at inversionally symmetric points with a phase shift of ∆φ = π in one of the bonds and no phase shift in the other one.…”

“…The Gaussian symplectic ensemble usually is associated with spin 1/2 systems, but Joyner et al [24] proposed an alternative way to realize the necessary condition T 2 = −1 in a graph with a peculiarly designed geometry. The proposal was experimentally realized in our group in a microwave network [25,26].…”

Universal S -matrix correlations for complex scattering of wave packets in noninteracting many-body systems: Theory, simulation, and experiment

“…[60][61][62] that the correlation functions of the S-matrix elements of open quantum graphs with a classically chaotic scattering dynamics coincide with the corresponding RMT results. Quantum graphs belonging to the orthogonal, the unitary, and the symplectic universality class have been realized experimentally with microwave networks consisting of coaxial cables connected by joints [55][56][57][58][59]63,64].…”

Transport studies in three-terminal microwave graphs with orthogonal, unitary, and symplectic symmetry

“…Furthermore, due to its intrinsic complexity, there are no scattering experiments up to now for systems with TRI and spin 1/2, where the signatures of the symplectic ensemble are expected, though there is one study of the spectral statistics in Au nanoparticles obeying this symmetry [19]. Moreover, very recently the appearance of a microwave experiment showing the signatures of the symplectic symmetry [20,21] for eigenvalue statistics has opened the possibility to study transport in the presence of this symmetry.Multiterminal devices are good candidates to provide experimental realizations for the three symmetry classes: Device Terminal 1 Terminal 2 Terminal 3 Junction FIG. 1.…”