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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. [ABSTRACT FROM AUTHOR]

Reflection and transmission measurements in microwave billiards with attached antennas allow the determination of all components of the scattering matrix including their phases. This is an extraordinary situation, since in usual scattering experiments in nuclear or atomic physics only reduced information such as the scattering cross-section can be obtained where the phase information is completely lost. This allows experimental tests of theoretical predictions of scattering theory inaccessible by any other method. As an example the distribution of reflection coefficients and of the line widths in a chaotic microwave billiard are discussed. [ABSTRACT FROM AUTHOR]

We analyze the echo dynamics in quasi-one-dimensional random media to investigate how the transition from localization to delocalization is encoded in its temporal decay properties. Our analysis extends from the standard perturbative regime corresponding to small perturbations (with respect to the mean level spacing) in the echo dynamics, out to the Wigner decay regime. On the theoretical side, our results rely on a banded random matrix modeling, and show in the localized regime under small perturbations a novel decay of the fidelity (Loschmidt echo), differing from the typical Gaussian decay seen within both diffusive and chaotic systems. For larger perturbation strengths, typical Wigner exponential decays are observed. Scattering echo measurements are performed experimentally within a quasi-1D microwave cavity randomly populated with point-like scatterers. Agreements are observed between experiments, numerics, and theoretical predictions. [ABSTRACT FROM AUTHOR]

We study the effects of single impurities on the transmission in microwave realizations of the photonic Kronig-Penney model, consisting of arrays of Teflon pieces alternating with air spacings in a microwave guide. As only the first propagating mode is considered, the system is essentially one-dimensional (1D) obeying the Helmholtz equation. We derive analytical closed form expressions from which the band structure, frequency of defect modes and band profiles can be determined. These agree very well with experimental data for all types of single defects considered (e.g. interstitial and substitutional) and show that our experimental set-up serves to explore some of the phenomena occurring in more sophisticated experiments. Conversely, based on the understanding provided by our formulae, information about the unknown impurity can be determined by simply observing certain features in the experimental data for the transmission. Further, our results are directly applicable to the closely related quantum 1D Kronig-Penney model. [ABSTRACT FROM AUTHOR]

Waves propagating through a weakly scattering random medium show a pronounced branching of the flow accompanied by the formation of freak waves, i.e., extremely intense waves. Theory predicts that this strong fluctuation regime is accompanied by its own fundamental length scale of transport in random media, parametrically different from the mean free path or the localization length. We show numerically how the scintillation index can be used to assess the scaling behavior of the branching length. We report the experimental observation of this scaling using microwave transport experiments in quasi-two-dimensional resonators with randomly distributed weak scatterers. Remarkably, the scaling range extends much further than expected from random caustics statistics. [ABSTRACT FROM AUTHOR]

Symmetry reduced three-disk and five-disk systems are studied in a microwave setup. Using harmonic inversion the distribution of the imaginary parts of the resonances is determined. With increasing opening of the systems, a spectral gap is observed for thick as well as for thin repellers and for the latter case it is compared with the known topological pressure bounds. The maxima of the distributions are found to coincide for a large range of the distance to radius parameter with half of the classical escape rate. This confirms theoretical predictions based on rigorous mathematical analysis for the spectral gap and on numerical experiments for the maxima of the distributions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]