Spectra and spectral correlations of microwave graphs with symplectic 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.

arXiv comment14 pages, 12 figures

References in corpus (8)

• Random-Matrix Theory of Quantum Transport
• Periodic Orbit Theory and Spectral Statistics for Quantum Graphs
• Experimental simulation of quantum graphs by microwave networks
• Periodic-orbit theory of universal level correlations in quantum chaos
• Power spectrum analysis and missing level statistics of microwave graphs with violated time reversal invariance
• A microwave realization of the Gaussian symplectic ensemble
• Inhomogeneous losses and complexness of wave functions in chaotic cavities
• GSE statistics without spin

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• Experimental investigation of distributions of the off-diagonal elements of the scattering and the Wigner's $\hat{K}$ matrices for networks with broken time reversal invariance
• Transport studies in three-terminal microwave graphs with orthogonal, unitary, and symplectic symmetry
• A spectral duality in graphs and microwave networks
• Microwave graphs analogs for the voltage drop in three-terminal devices with orthogonal, unitary and symplectic symmetry
• Universal S-matrix correlations for complex scattering of many-body wavepackets: theory, simulation and experiment
• Missing level statistics in a dissipative microwave resonator with partially violated time-reversal invariance
• Superuniversal Statistics of Complex Time-Delays in Non-Hermitian Scattering Systems
• Experimental Realization of Anti-Unitary Wave-Chaotic Photonic Topological Insulator Graphs Showing Kramers Degeneracy and Symplectic Ensemble Statistics
• Microwave studies of the three chiral ensembles in chains of coupled dielectric resonators
• Experimental study of the distributions of off-diagonal scattering-matrix elements of quantum graphs with symplectic symmetry
• Superuniversal Statistics with Topological Origins for non-Hermitian Scattering Singularities
• Scarring in open chaotic systems: The local density of states