Microwave Studies of Three Chiral Ensembles in Chains of Coupled Dielectric Resonators |
| M. Richtera, b, c, A. Rehemanjiangd, U. Kuhlc, H.J. Stöckmannd
aSchool of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom bSchool of Science and Technology, Nottingham Trent University, Nottingham NG11 8NS, United Kingdom cUniversité Côte d'Azur, CNRS, Institut de Physique de Nice (INPHYNI), 06108 Nice, France dFachbereich Physik der Philipps-Universität Marburg, D-35032 Marburg, Germany |
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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, Gaussian unitary, and Gaussian symplectic 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 which are the main point of interest in this paper. Following a recently published work on chiral random matrix ensembles and their experimental realizations, Phys. Rev. Lett. 124, 116801 (2020), this is achieved by using dielectric cylinders placed between two parallel aluminium plates. These cylinders act as microwave resonators which are used to create tight-binding chains of finite length up to N=5. The different ensembles are achieved by using different types of couplings: (i) for the orthogonal case spatial proximity is used, for the unitary case microwave circulators are used, and (ii) for the symplectic case a combination of circulators and cables is used to create the necessary symmetry. In all cases the predicted repulsion behavior between positive and negative eigenvalues for energies close to zero are verified by a comparison with theory taking the finite size of the systems into account. We will show that the difference to the expected universal behavior is given by logarithmic corrections only. These corrections stem from the Hamiltonians having zero entries in their off-diagonal blocks. |
DOI:10.12693/APhysPolA.140.492 topics: wave chaos, random matrix theory, chiral systems, topological materials |