Related Experiment Video
Updated: Dec 25, 2025

Author Spotlight: Unveiling the Potential of VSFG Microscopy in Studying Mesoscopically Heterogeneous Self-Assembled Structures
Published on: December 1, 2023
Microwave Realization of the Chiral Orthogonal, Unitary, and Symplectic Ensembles
A Rehemanjiang1, M Richter2,3,4, U Kuhl1,4
1Fachbereich Physik der Philipps-Universität Marburg, D-35032 Marburg, Germany.
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.
Related Concept Videos
Racemic Mixtures and the Resolution of Enantiomers
¹H NMR Chemical Shift Equivalence: Enantiotopic and Diastereotopic Protons
In chiral compounds such as 2-butanol, replacing the methylene hydrogens at C3 produces a pair of...
Chirality in Nature
Molecules with Multiple Chiral Centers
Properties of Enantiomers and Optical Activity
Stereoisomerism
Isomers are different chemical species that have the same chemical formula.
Transition metal complexes often exist as geometric isomers, in which the same atoms are connected through the same types of bonds but with differences in their orientation in space. Coordination complexes with two different ligands in the cis and trans positions from a ligand of interest form isomers. For example, the octahedral [Co(NH3)4Cl2]+ ion has two isomers (Figure 1) In the cis...

