GSE statistics without spin

Abstract

Energy levels statistics following the Gaussian Symplectic Ensemble (GSE) of Random Matrix Theory have been predicted theoretically and observed numerically in numerous quantum chaotic systems. However in all these systems there has been one unifying feature: the combination of half-integer spin and time-reversal invariance. Here we provide an alternative mechanism for obtaining GSE statistics that is based on geometric symmetries of a quantum system which alleviates the need for spin. As an example, we construct a quantum graph with a particular discrete symmetry given by the quaternion group Q8. GSE statistics is then observed within one of its subspectra.

5 pages, 6 figures

References in corpus (3)

• Are Scattering Properties of Graphs Uniquely Connected to Their Shapes?
• The Isospectral Fruits of Representation Theory: Quantum Graphs and Drums
• Semiclassical approach to discrete symmetries in quantum chaos

Cited by in corpus (10)

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• Spectra and spectral correlations of microwave graphs with symplectic symmetry
• A spectral duality in graphs and microwave networks
• Spectral Properties of Quantum Circulant Graphs
• Closed and open superconducting microwave waveguide networks as a model for quantum graphs
• Periodic orbit evaluation of a spectral statistic of quantum graphs without the semiclassical limit
• Experimental Realization of Anti-Unitary Wave-Chaotic Photonic Topological Insulator Graphs Showing Kramers Degeneracy and Symplectic Ensemble Statistics
• GSE spectra in uni-directional quantum systems
• Microwave studies of the three chiral ensembles in chains of coupled dielectric resonators
• Convergence of moments of twisted COE matrices