Microwave Realization of the Gaussian Symplectic Ensemble

Rehemanjiang, A.; Allgaier, Markus; Joyner, Christopher H.; Müller, Sebastian; Sieber, Martin; Kuhl, Ulrich; Stöckmann, H.‐J.

doi:10.1103/physrevlett.117.064101

Cited by 69 publications

(62 citation statements)

References 29 publications

(33 reference statements)

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“…In our recent paper [12] we presented first results on spectra in a microwave graph with symplectic symmetry. The Kramers doublets expected for such a system had been clearly observed, and their level spacing distribution could be well described by the GSE Wigner distribution.…”

Section: Discussionmentioning

confidence: 99%

“…There are altogether only three studies of the spectra of systems with broken TRS showing GUE statistics [9][10][11], all of them applying microwave techniques. For the GSE there is as yet only one recent experimental realization by our group [12]. In the present paper a more detailed account on the latter work is given, as well as a number of new results.…”

Section: Introductionmentioning

confidence: 85%

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Spectra and spectral correlations of microwave graphs with symplectic symmetry

Rehemanjiang¹,

Richter²,

Kuhl³

et al. 2018

Phys. Rev. E

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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.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 85%

Spectra and spectral correlations of microwave graphs with symplectic symmetry

Rehemanjiang¹,

Richter²,

Kuhl³

et al. 2018

Phys. Rev. E

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“…7, but for the GUE the number of experiments is still small [8][9][10]. The GSE has been realized only recently by us in a peculiarly designed microwave network mimicking a spin 1/2 [11].For the new ensembles systematic random matrix studies are still missing though there are a lot of studies of systems showing chiral symmetry [12]. In the present work a microwave study of the chiral relatives of the classical ensembles shall be presented, the chiral orthogonal (chOE), the chiral unitary (chUE), and the chiral symplectic (chSE) ensemble (the BDI, the AIII, and the CII in Cartan's notation).…”

mentioning

confidence: 99%

“…7, but for the GUE the number of experiments is still small [8][9][10]. The GSE has been realized only recently by us in a peculiarly designed microwave network mimicking a spin 1/2 [11].…”

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confidence: 99%

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

et al. 2020

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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. PACS numbers: 05.45.MtRandom matrix theory originally had been developed by Wigner, Dyson, Mehta [1, 2] and others as a tool to describe the spectral properties of chaotic systems. For time-reversal symmetric systems the Hamiltonian H commutes with the time-reversal operator T , HT = T H, where T 2 = 1 for systems without spin 1/2, and T 2 = −1 in the presence of a spin 1/2 [3]. The three options (T 2 = 1, no T , T 2 = −1) give rise to the three classical random matrix ensembles, the Gaussian orthogonal (GOE), unitary (GUE) and symplectic (GSE) one, respectively. Further there may be a chiral symmetry, i. e., an operator C anticommuting with H, HC = −CH, again with the two options C 2 = 1 and C 2 = −1. Such a symmetry exists, e. g., for the Dirac equation [4]. All possible combinations of (T 2 = 1, no T , T 2 = −1) and (C 2 = 1, no C, C 2 = −1) yield a total of nine random matrix ensembles. Together with the last remaining option (no T , no C, but CT ) one finally ends up with the ten-fold way [5,6].For the GOE there is an abundant number of realizations, see Sec. 3.2 of Ref. 7, but for the GUE the number of experiments is still small [8][9][10]. The GSE has been realized only recently by us in a peculiarly designed microwave network mimicking a spin 1/2 [11].For the new ensembles systematic random matrix studies are still missing though there are a lot of studies of systems showing chiral symmetry [12]. In the present work a microwave study of the chiral relatives of the classical ensembles shall be presented, the chiral orthogonal (chOE), the chiral unitary (chUE), and the chiral symplectic (chSE) ensemble (the BDI, the AIII, and the CII in Cartan's notation). We omit the 'G' in the notation, since the ensembles studied by us are partly not Gaussian.For a chiral symmetry particles and anti-particles are not really needed. Sufficient is a system consisting of two subsystems I and II with interactions only between I and II, but no internal interactions within I or II. The Hamiltonian for such a situation may be written aswhere the diagonal blocks belong to the two subsystems, and the off-diagonal blocks describe the interaction. Hamiltonian (1) is chiral symmetric, since it anticommutes with C = diag(1 n , −1 m ). The characteristic polynomial of ...

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Covert Scattering Control in Metamaterials with Non‐Locally Encoded Hidden Symmetry

Sol,

Röntgen,

del Hougne

2023

Advanced Materials

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Symmetries and tunability are of fundamental importance in wave scattering control, but symmetries are often obvious upon visual inspection which constitutes a significant vulnerability of metamaterial wave devices to reverse‐engineering risks. Here, it is theoretically and experimentally shown that a symmetry in the reduced basis of the “primary meta‐atoms” that are directly connected to the outside world is sufficient; meanwhile, a suitable topology of non‐local interactions between them, mediated by the internal “secondary” meta‐atoms, can hide the symmetry from sight in the canonical basis. Covert symmetry‐based scattering control in a cable‐network metamaterial featuring a hidden parity () symmetry in combination with hidden‐‐symmetry‐preserving and hidden‐‐symmetry‐breaking tuning mechanisms is experimentally demonstrated. Physical‐layer security in wired communications is achieved, using the domain‐wise hidden ‐symmetry as shared secret between the sender and the legitimate receiver. Within the approximation of negligible absorption, the first tuning of a complex scattering metamaterial without mirror symmetry to feature exceptional points (EPs) of ‐symmetric reflectionless states, as well as quasi‐bound states in the continuum, is reported. These results are reproduced in metamaterials involving non‐reciprocal interactions between meta‐atoms, including the first observation of reflectionless EPs in a non‐reciprocal system.This article is protected by copyright. All rights reserved

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Microwave Realization of the Gaussian Symplectic Ensemble

Cited by 69 publications

References 29 publications

Spectra and spectral correlations of microwave graphs with symplectic symmetry

Spectra and spectral correlations of microwave graphs with symplectic symmetry

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

Covert Scattering Control in Metamaterials with Non‐Locally Encoded Hidden Symmetry

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