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

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