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

TL;DR

This paper demonstrates a microwave-based experimental setup that models the spectral properties of chiral random matrix ensembles, verifying theoretical predictions about eigenvalue repulsion near zero energy.

Contribution

It provides the first microwave realization of chiral orthogonal, unitary, and symplectic ensembles, confirming key spectral features predicted by theory.

Findings

Verified eigenvalue repulsion near zero energy in all three chiral ensembles

Successfully modeled chiral ensembles using coupled dielectric resonators

Confirmed theoretical spectral behavior through microwave experiments

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.