A microwave realization of the chiral orthogonal, unitary, and symplectic ensembles

Abstract

Random matrix theory has proven very successful in the understanding of the spectra of chaotic systems. Depending on symmetry with respect to time reversal and the presence or absence of a spin 1/2 there are three ensembles, the Gaussian orthogonal (GOE), Gaussian unitary (GUE), and Gaussian symplectic (GSE) one. With a further particle-antiparticle symmetry the chiral variants of these ensembles, the chiral orthogonal, unitary, and symplectic ensembles (the BDI, AIII, and CII in Cartan's notation) appear. A microwave study of the chiral ensembles is presented using a linear chain of evanescently coupled dielectric cylindrical resonators. In all cases the predicted repulsion behavior between positive and negative eigenvalues for energies close to zero could be verified.

arXiv comment5 pages, 5 figures

References in corpus (17)

• Topological Insulators
• Topological Photonics
• Topological Photonics
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Riemannian symmetric superspaces and their origin in random matrix theory
• The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way
• Spectral Density of the QCD Dirac Operator near Zero Virtuality
• Random-matrix theory of Majorana fermions and topological superconductors
• Tight-binding couplings in microwave artificial graphene
• A microwave realization of the Gaussian symplectic ensemble
• Resonance widths in open microwave cavities studied by harmonic inversion
• Use of Harmonic Inversion Techniques in Semiclassical Quantization and Analysis of Quantum Spectra
• The supersymmetric technique for random-matrix ensembles with zero eigenvalues
• Disordered graphene and boron nitride in a microwave tight-binding analog
• Microwave studies of the three chiral ensembles in chains of coupled dielectric resonators

Cited by in corpus (12)

• Missing-level statistics in classically chaotic quantum systems with symplectic symmetry
• Non-Hermitian CT-Symmetric Spectral Protection of Nonlinear Defect Modes
• Engineering Interaction Dynamics in Active Resonant Photonic Structures
• Superposition and higher-order spacing ratios in random matrix theory with application to complex systems
• Metal-insulator transition in a 2D system of chiral unitary class
• Transport in deformed centrosymmetric networks
• Experimental study of closed and open microwave waveguide graphs with preserved and partially violated time-reversal invariance
• Eigenfunction and eigenmode-spacing statistics in chaotic photonic crystal graphs
• Closed and open superconducting microwave waveguide networks as a model for quantum graphs
• Universal scaling of higher-order spacing ratios in Gaussian random matrices
• Experimental Realization of Anti-Unitary Wave-Chaotic Photonic Topological Insulator Graphs Showing Kramers Degeneracy and Symplectic Ensemble Statistics
• Numerical Investigation of Localization in Two-Dimensional Quasiperiodic Mosaic Lattice