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Microwave Realization of the Chiral Orthogonal, Unitary, and Symplectic Ensembles

Rehemanjiang, A.; Richter, M.; Kuhl, U.; St�ckmann, H.-J.

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Authors

A. Rehemanjiang

MARTIN RICHTER MARTIN.RICHTER@NOTTINGHAM.AC.UK
Assistant Professor in Applied Mathematics

U. Kuhl

H.-J. St�ckmann



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. We exhibit a microwave setup based on a linear chain of evanescently coupled dielectric cylindrical resonators allowing us to study all three chiral ensembles experimentally. In all cases the predicted repulsion behavior between positive and negative eigenvalues for energies close to zero could be verified.

Citation

Rehemanjiang, A., Richter, M., Kuhl, U., & Stöckmann, H. (2020). Microwave Realization of the Chiral Orthogonal, Unitary, and Symplectic Ensembles. Physical Review Letters, 124(11), Article 116801. https://doi.org/10.1103/physrevlett.124.116801

Journal Article Type Article
Acceptance Date Feb 24, 2020
Online Publication Date Mar 16, 2020
Publication Date Mar 20, 2020
Deposit Date Nov 6, 2020
Publicly Available Date Mar 28, 2024
Journal Physical Review Letters
Print ISSN 0031-9007
Electronic ISSN 1079-7114
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 124
Issue 11
Article Number 116801
DOI https://doi.org/10.1103/physrevlett.124.116801
Keywords General Physics and Astronomy
Public URL https://nottingham-repository.worktribe.com/output/5020482
Publisher URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.116801
Additional Information © 2020 American Physical Society.

Preprint:
https://arxiv.org/abs/1909.12886

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