Search

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]

Reverberation chambers are currently used to test electromagnetic compatibility as well as to characterize antenna efficiency, wireless devices, and MIMO systems. The related measurements are based on statistical averages and their fluctuations. We introduce a very efficient mode stirring process based on electronically reconfigurable metasurfaces (ERMs). By locally changing the field boundary conditions, the ERMs allow us to generate a humongous number of uncorrelated field realizations even within small reverberation chambers. We fully experimentally characterize this stirring process by determining these uncorrelated realizations via the autocorrelation function of the transmissions. The uniformity criterion parameter σ dB , as defined in the IEC 61000-4-21 standard, is also investigated and reveals the performance of this stirring. The effect of short paths on the two presented quantities is identified. We compare the experimental results on the uniformity criterion parameter with a corresponding model based on random matrix theory and find good agreement, where the only parameter, the modal overlap, is extracted by the quality factor. [ABSTRACT FROM AUTHOR]

We present a microwave realization of a reflective topological limiter based on an explicit self-induced violation of a charge-conjugation (CT) symmetry. The starting point is a bipartite structure created by coupled dielectric resonators with a topological defect placed at the center and two lossy resonators placed on the neighboring sites of the defect. This defect supports a resonant mode if the CT -symmetry is present, while it is suppressed once the symmetry is violated due to permittivity changes of the defect resonator associated with high irradiances of the incident radiation. This destruction leads to a suppression of transmittance and a subsequent increase of the reflectance while the absorption is also suppressed. [ABSTRACT FROM AUTHOR]

In this review article, we will demonstrate the power of microwave experiments in the realm of fidelity also known as Loschmidt echoes. As the determination of the fidelity itself is experimentally tedious and error prone, we will introduce the scattering fidelity which under the conditions of chaotic systems and weak coupling approaches the fidelity itself. The main ingredient in fidelity investigations is the type and strength of a perturbation. The perturbations presented here will be both global and local boundary perturbations, as well as local perturber movements but also the change of coupling to the environment. All these perturbations will produce their own fidelity decay as a function of the perturbation strength, which will be discussed in this article. [ABSTRACT FROM AUTHOR]

The change of resonance widths in an open system under a perturbation of its interior has been recently introduced by Fyodorov and Savin [Phys. Rev. Lett. 108, 184101 (2012)] as a sensitive indicator of the nonorthogonality of resonance states. We experimentally study universal statistics of this quantity in weakly open two-dimensional microwave cavities and reverberation chambers realizing scalar and electromagnetic vector fields, respectively. We consider global as well as local perturbations, and also extend the theory to treat the latter case. The influence of the perturbation type on the width shift distribution is more pronounced for many-channel systems. We compare the theory to experimental results for one and two attached antennas and to numerical simulations with higher channel numbers, observing a good agreement in all cases. [ABSTRACT FROM AUTHOR]

A schematic model for baryon excitations is presented in terms of a symmetric Dirac gyroscope, a relativistic model solvable in closed form, that reduces to a rotor in the non-relativistic limit. The model is then mapped on a nearest neighbour tight binding model. In its simplest one-dimensional form this model yields a finite equidistant spectrum. This is experimentally implemented as a chain of dielectric resonators under conditions where their coupling is evanescent and a good agreement with the prediction is achieved. [ABSTRACT FROM AUTHOR]

A realization of a periodically driven microwave system is presented. The principal element of the scheme is a variable capacity, i.e. a varicap, introduced as an element of the resonant circuit. Sideband structures, corresponding to different driving signals, have been measured experimentally. In the linear regime we observed sideband structures with specific shapes. The main peculiarities of these shapes can be explained within a semiclassical approximation. A good agreement between experimental data and theoretical expectations has been found. [ABSTRACT FROM AUTHOR]

The description of open quantum system successfully uses the concept of the effective Hamiltonian, which takes into account the coupling to the environment. The concept can be extended to classical waves. Experimentally, classical waves are very convenient as they allow to control boundaries, coupling and absorption. We combine here recent works with microwaves investigating properties of open systems which can be described by an effective Hamiltonian. This ranges from spectral properties like modifications to level dynamics, width distribution and coupling fidelity to spatial properties like intensity distributions and complexness parameter which describes the non-orthogonality of eigenfunctions. [ABSTRACT FROM AUTHOR]

We analyse the single-mode transmission of microwaves in a guide with internal random structure. The waveguide contains scatterers characterized by random heights and positions, corresponding to compositional and structural disorder. We measure the effects of cross-correlations between two kinds of disorder, showing how they enhance or attenuate the experimentally found transmission gaps generated by long-range self-correlations. The results agree with the theoretical predictions obtained for the aperiodic Kronig-Penney model and prove that self- and cross-correlations also have relevant effects in finite disordered samples of small size. [ABSTRACT FROM AUTHOR]

A microwave setup for mode-resolved transport measurement in quasi-one-dimensional (quasi-1D) structures is presented. We will demonstrate a technique for direct measurement of the Green's function of the system. With its help we will investigate quasi-1D structures with various types of disorder. We will focus on stratified structures, i.e., structures that are homogeneous perpendicular to the direction of wave propagation. In this case the interaction between different channels is absent, so wave propagation occurs individually in each open channel. We will apply analytical results developed in the theory of one-dimensional (1D) disordered models in order to explain main features of the transport. The main focus will be selective transport due to long-range correlations in the disorder. In our setup, we can intentionally introduce correlations by changing the positions of periodically spaced brass bars of finite thickness. Because of the equivalence of the stationary Schrödinger equation and the Helmholtz equation, the result can be directly applied to selective electron transport in nanowires, nanostripes, and superlattices. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the 'singular statistics' of pseudointegrable Šeba billiards, i.e. billiards perturbed by zero-range perturbations. We have shown that the computation of a spectrum is reduced to the calculation of the uniquely defined renormalized Green's function. We relate a spectrum of the billiard to the scattering length, which is the only parameter describing the perturbation. We show that taking into account the growing number of resonances, one observes a transition from 'semi-Poissonian'-like statistics to Poissonian. This observation is in agreement with the argument that a classical particle does not feel a point perturbation. [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]

Abstract: We perform a power spectrum analysis of energy level fluctuations in experimental quantum Sinai billiards. In spite of experimental limitations we find the behavior expected for quantum chaotic systems. Moreover, the deviations observed at low frequencies are easily explained within the semiclassical periodic orbit theory. In conclusion, it is shown that the power spectrum analysis of energy level fluctuations is a robust signature of quantum chaos. [Copyright &y& Elsevier]

Experimental and clinical data suggest a relationship between myocarditis and dilated cardiomyopathy. One postulated mechanism is a viral infection triggering a host response with autoimmune features directed against the heart, resulting in an initial myocarditis which is followed by dilated cardiomyopathy. Until now, the importance of myocarditis as an aetiological factor in the pathogenesis of isiopathic cardiomyopathy has been unknown. This investigation was undertaken to determine immunohistologically the frequency of lymphocytic infiltrations in endomyocardial biopsies of patients with clinically suspected dilated cardiomyopathy. T-lymphocytic subsets and other immunological features were also analysed to explore possible relationships between immunohistologically documented myocarditis and dilated cardiomyopathy. [ABSTRACT FROM PUBLISHER]

We propose a concept of chiral photonic limiters utilizing topologically protected localized midgap defect states in a photonic waveguide. The chiral symmetry alleviates the effects of structural imperfections and guarantees a high level of resonant transmission for low intensity radiation. At high intensity, the light-induced absorption can suppress the localized modes, along with the resonant transmission. In this case the entire photonic structure becomes highly reflective within a broad frequency range, thus increasing dramatically the damage threshold of the limiter. Here, we demonstrate experimentally the loss-induced reflection principle of operation which is at the heart of reflective photonic limiters using a waveguide consisting of coupled dielectric microwave resonators. [ABSTRACT FROM AUTHOR]

The effective Hamiltonian formalism is extended to vectorial electromagnetic waves in order to describe statistical properties of the field in reverberation chambers. The latter are commonly used in electromagnetic compatibility tests. As a first step, the distribution of wave intensities in chaotic systems with varying opening in the weak coupling limit for scalar quantum waves is derived by means of random matrix theory. In this limit the only parameters are the modal overlap and the number of open channels. Using the extended effective Hamiltonian, we describe the intensity statistics of the vectorial electromagnetic eigenmodes of lossy reverberation chambers. Finally, the typical quantity of interest in such chambers, namely, the distribution of the electromagnetic response, is discussed. By determining the distribution of the phase rigidity, describing the coupling to the environment, using random matrix numerical data, we find good agreement between the theoretical prediction and numerical calculations of the response. [ABSTRACT FROM AUTHOR]

The tight-binding model with correlated disorder introduced by Izrailev and Krokhin [Phys. Rev. Lett. 82, 4062 (1999)] has been extended to the Kronig-Penney model. The results of the calculations have been compared with microwave transmission spectra through a single-mode waveguide with inserted correlated scatterers. All predicted bands and mobility edges have been found in the experiment, thus demonstrating that any wanted combination of transparent and nontransparent frequency intervals can be realized experimentally by introducing appropriate correlations between scatterers. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Experiments on hexagonal graphene-like structures using microwave measuring techniques are presented. The lowest transverse-electric resonance of coupled dielectric disks sandwiched between two metallic plates establishes a tight-binding configuration. The nearest-neighbor coupling approximation is investigated in systems with few disks. Taking advantage of the high flexibility of the disks positions, consequences of the disorder introduced in the graphene lattice on the Dirac points are investigated. Using two different types of disks, a boron-nitride-like structure (a hexagonal lattice with a two-atom basis) is implemented, showing the appearance of a band gap. [ABSTRACT FROM AUTHOR]

The boundaries of waveguides and nanowires have drastic influence on their coherent scattering properties. Designing the boundary profile is thus a promising approach for transmission and band-gap engineering with many applications. By performing an experimental study of microwave transmission through rough waveguides we demonstrate that a recently proposed surface scattering theory can be employed to predict the measured transmission properties from the boundary profiles and vice versa. A new key ingredient of this theory is a scattering mechanism which depends on the squared gradient of the surface profiles. We demonstrate the nontrivial effects of this scattering mechanism by detailed mode-resolved microwave measurements and numerical simulations. [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]

Following an idea by Joyner et al. [Europhys. Lett. 107, 50004 (2014)], a microwave graph with antiunitary symmetry T obeying T²=-1 has been realized, thus mimicking a spin-1/2 system. The Kramers doublets expected for such systems have been clearly identified and could be lifted by a perturbation which breaks the antiunitary symmetry. The observed spectral level-spacing distribution of the Kramers doublets agreed with the predictions from the Gaussian symplectic ensemble (GSE), expected for chaotic systems with such a symmetry. In addition, we studied the random matrix equivalents of the used graphs both analytically and numerically. Here small deviations from the GSE level-spacing distribution were found, too small to be seen in the experiment but clearly visible in the simulations. Furthermore, results on the two-point correlation function, the spectral form factor, the number variance, and the spectral rigidity are presented, as well as on the transition from Gaussian symplectic to Gaussian orthogonal statistics by continuously changing T from T²=-1 to T²=1. [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]

We present the first experimental microwave realization of the one-dimensional Dirac oscillator, a paradigm in exactly solvable relativistic systems. The experiment relies on a relation of the Dirac oscillator to a corresponding tight-binding system. This tight-binding system is implemented as a microwave system by a chain of coupled dielectric disks, where the coupling is evanescent and can be adjusted appropriately. The resonances of the finite microwave system yield the spectrum of the one-dimensional Dirac oscillator with and without a mass term. The flexibility of the experimental setup allows the implementation of other one-dimensional Dirac-type equations. [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]

Following an idea by Joyner et al. [Europhys. Lett. 107, 50004 (2014)], a microwave graph with an antiunitary symmetry T obeying T²=-1 is realized. The Kramers doublets expected for such systems are clearly identified and can be lifted by a perturbation which breaks the antiunitary symmetry. The observed spectral level spacings distribution of the Kramers doublets is in agreement with the predictions from the Gaussian symplectic ensemble expected for chaotic systems with such a symmetry. [ABSTRACT FROM AUTHOR]