Failure of the Conformal-Map Method for Relativistic Quantum Billiards.

In H. Xu et al. [Phys.

Closed and open superconducting microwave waveguide networks as a model for quantum graphs.

We report on high-precision measurements that were performed with superconducting waveguide networks with the geometry of a tetrahedral and a honeycomb graph. They consist of junctions of valency three that connect straight rectangular waveguides of equal width but incommensurable lengths. The experiments were performed in the frequency range of a single transversal mode, where the associated Helmholtz equation is effectively one-dimensional and waveguide networks may serve as models of quantum graphs with the joints and waveguides corresponding to the vertices and bonds.

Experimental test of the Rosenzweig-Porter model for the transition from Poisson to Gaussian unitary ensemble statistics.

We report on an experimental investigation of the transition of a quantum system with integrable classical dynamics to one with violated time-reversal (T) invariance and chaotic classical counterpart. High-precision experiments are performed with a flat superconducting microwave resonator with circular shape in which T-invariance violation and chaoticity are induced by magnetizing a ferrite disk placed at its center, which above the cutoff frequency of the first transverse-electric mode acts as a random potential. We determine a complete sequence of ≃1000 eigenfrequencies and find good agreement with analytical predictions for the spectral properties of the Rosenzweig-Porter (RP) model, which interpolates between Poisson statistics expected for typical integrable systems and Gaussian unitary ensemble statistics predicted for chaotic systems with violated Tinvariance.

Experimental study of the elastic enhancement factor in a three-dimensional wave-chaotic microwave resonator exhibiting strongly overlapping resonances.

We study the elastic enhancement factor and the two-point correlation function of the scattering matrix obtained from measurements of reflection and transmission spectra of a three-dimensional (3D) wave-chaotic microwave cavity in regions of moderate and large absorption. They are used to identify the degree of chaoticity of the system in the presence of strongly overlapping resonances, where other measures such as short- and long-range level correlations cannot be applied. The average value of the experimentally determined elastic enhancement factor for two scattering channels agrees well with random-matrix theory predictions for quantum chaotic systems, thus corroborating that the 3D microwave cavity exhibits the features of a fully chaotic system with preserved time-reversal invariance.

Semi-Poisson Statistics in Relativistic Quantum Billiards with Shapes of Rectangles.

Rectangular billiards have two mirror symmetries with respect to perpendicular axes and a twofold (fourfold) rotational symmetry for differing (equal) side lengths. The eigenstates of rectangular neutrino billiards (NBs), which consist of a spin-1/2 particle confined through boundary conditions to a planar domain, can be classified according to their transformation properties under rotation by π (π/2) but not under reflection at mirror-symmetry axes. We analyze the properties of these symmetry-projected eigenstates and of the corresponding symmetry-reduced NBs which are obtained by cutting them along their diagonal, yielding right-triangle NBs.

Distributions of the Wigner reaction matrix for microwave networks with symplectic symmetry in the presence of absorption.

We report on experimental studies of the distribution of the reflection coefficients, and the imaginary and real parts of Wigner's reaction (K) matrix employing open microwave networks with symplectic symmetry and varying size of absorption. The results are compared to analytical predictions derived for the single-channel scattering case within the framework of random-matrix theory (RMT). Furthermore, we performed Monte Carlo simulations based on the Heidelberg approach for the scattering (S) and K matrix of open quantum-chaotic systems and the two-point correlation function of the S-matrix elements.

Entanglement Dynamics and Classical Complexity.

We study the dynamical generation of entanglement for a two-body interacting system, starting from a separable coherent state. We show analytically that in the quasiclassical regime the entanglement growth rate can be simply computed by means of the underlying classical dynamics. Furthermore, this rate is given by the Kolmogorov-Sinai entropy, which characterizes the dynamical complexity of classical motion.

Experimental study of closed and open microwave waveguide graphs with preserved and partially violated time-reversal invariance.

We report on experiments that were performed with microwave waveguide systems and demonstrate that in the frequency range of a single transversal mode they may serve as a model for closed and open quantum graphs. These consist of bonds that are connected at vertices. On the bonds, they are governed by the one-dimensional Schrödinger equation with boundary conditions imposed at the vertices.

Fluctuation properties of the eigenfrequencies and scattering matrix of closed and open unidirectional graphs with chaotic wave dynamics.

We present experimental and numerical results for the fluctuation properties in the eigenfrequency spectra and of the scattering matrix of closed and open unidirectional quantum graphs, respectively. Unidirectional quantum graphs, that are composed of bonds connected by reflectionless vertices, were introduced by Akila and Gutkin [Akila and Gutkin, J. Phys.

Möbius Strip Microlasers: A Testbed for Non-Euclidean Photonics.

We report on experiments with Möbius strip microlasers, which were fabricated with high optical quality by direct laser writing. A Möbius strip, i.e.

Universal S-matrix correlations for complex scattering of wave packets in noninteracting many-body systems: Theory, simulation, and experiment.

We present an in-depth study of the universal correlations of scattering-matrix entries required in the framework of nonstationary many-body scattering of noninteracting indistinguishable particles where the incoming states are localized wave packets. Contrary to the stationary case, the emergence of universal signatures of chaotic dynamics in dynamical observables manifests itself in the emergence of universal correlations of the scattering matrix at different energies. We use a semiclassical theory based on interfering paths, numerical wave function based simulations, and numerical averaging over random-matrix ensembles to calculate such correlations and compare with experimental measurements in microwave graphs, finding excellent agreement.

Missing-level statistics in a dissipative microwave resonator with partially violated time-reversal invariance.

We report on the experimental investigation of the fluctuation properties in the resonance frequency spectra of a flat resonator simulating a dissipative quantum billiard subject to partial time-reversal-invariance violation (TIV) which is induced by two magnetized ferrites. The cavity has the shape of a quarter bowtie billiard of which the corresponding classical dynamics is chaotic. Due to dissipation it is impossible to identify a complete list of resonance frequencies.

Missing-level statistics in classically chaotic quantum systems with symplectic symmetry.

We present experimental and theoretical results for the fluctuation properties in the incomplete spectra of quantum systems with symplectic symmetry and a chaotic dynamics in the classical limit. To obtain theoretical predictions, we extend the random-matrix theory (RMT) approach introduced in Bohigas and Pato [O. Bohigas and M.

Semiclassical quantization of neutrino billiards.

The impact of the classical dynamic on the fluctuation properties in the eigenvalue spectrum of nonrelativistic quantum billiards (QBs) are now well understood based on the semiclassical approach which provides an approximation for the fluctuating part ρ^{fluc}(k) of the spectral density in terms of a trace formula, that is, a sum over classical periodic orbits of its classical counterpart, abbreviated as CB. This connection between the eigenvalue spectrum of a quantum system and the classical periodic orbits is discernible in the Fourier transform of ρ^{fluc}(k) from eigenwave number k to length, which exhibits peaks at the lengths of the periodic orbits. The uprise of interest in properties of graphene related to their relativistic Dirac spectrum implicated the emergence of intensive studies of relativistic neutrino billiards (NBs), consisting of a spin-1/2 particle governed by the Dirac equation and confined to a bounded planar domain.

How time-reversal-invariance violation leads to enhanced backscattering with increasing openness of a wave-chaotic system.

We report on the experimental investigation of the dependence of the elastic enhancement, i.e., enhancement of scattering in the backward direction over scattering in other directions, of a wave-chaotic system with partially violated time-reversal (T) invariance on its openness.

Experimental and numerical investigation of parametric spectral properties of quantum graphs with unitary or symplectic symmetry.

We present experimental and numerical results for the parametric fluctuation properties in the spectra of classically chaotic quantum graphs with unitary or symplectic symmetry. A level dynamics is realized by changing the lengths of a few bonds parametrically. The long-range correlations in the spectra reveal at a fixed parameter value deviations from those expected for generic chaotic systems with corresponding universality class.

Kac's isospectrality question revisited in neutrino billiards.

"Can one hear the shape of a drum?" Kac raised this famous question in 1966, referring to the possibility of the existence of nonisometric planar domains with identical Dirichlet eigenvalue spectra of the Laplacian. Pairs of nonisometric isospectral billiards were eventually found by employing the transplantation method which was deduced from Sunada's theorem. Our main focus is the question to what extent isospectrality of nonrelativistic quantum billiards is present in the corresponding relativistic case, i.

Experimental investigation of the elastic enhancement factor in a microwave cavity emulating a chaotic scattering system with varying openness.

A characteristic of chaotic scattering is the excess of elastic over inelastic scattering processes quantified by the elastic enhancement factor F_{M}(T,γ), which depends on the number of open channels M, the average transmission coefficient T, and internal absorption γ. Using a microwave cavity with the shape of a chaotic quarter-bow-tie billiard, we study the elastic enhancement factor experimentally as a function of the openness, which is defined as the ratio of the Heisenberg time and the Weisskopf (dwell) time and is directly related to M and the size of internal absorption. In the experiments 2≤M≤9 open channels with an average transmission coefficient 0.

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison.

The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal cross sections in the Heidelberg approach, which is applicable to a wide range of quantum chaotic systems. Thus, eventually, we fully solve a problem that already arose more than half a century ago in compound-nucleus scattering.

Chemotherapy Extravasation: Establishing a National Benchmark for Incidence Among Cancer Centers.

Background: Given the high-risk nature and nurse sensitivity of chemotherapy infusion and extravasation prevention, as well as the absence of an industry benchmark, a group of nurses studied oncology-specific nursing-sensitive indicators. 
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Objectives: The purpose was to establish a benchmark for the incidence of chemotherapy extravasation with vesicants, irritants, and irritants with vesicant potential.

Nonuniversality in the spectral properties of time-reversal-invariant microwave networks and quantum graphs.

We present experimental and numerical results for the long-range fluctuation properties in the spectra of quantum graphs with chaotic classical dynamics and preserved time-reversal invariance. Such systems are generally believed to provide an ideal basis for the experimental study of problems originating from the field of quantum chaos and random matrix theory. Our objective is to demonstrate that this is true only for short-range fluctuation properties in the spectra, whereas the observation of deviations in the long-range fluctuations is typical for quantum graphs.

Gaussian orthogonal ensemble statistics in graphene billiards with the shape of classically integrable billiards.

A crucial result in quantum chaos, which has been established for a long time, is that the spectral properties of classically integrable systems generically are described by Poisson statistics, whereas those of time-reversal symmetric, classically chaotic systems coincide with those of random matrices from the Gaussian orthogonal ensemble (GOE). Does this result hold for two-dimensional Dirac material systems? To address this fundamental question, we investigate the spectral properties in a representative class of graphene billiards with shapes of classically integrable circular-sector billiards. Naively one may expect to observe Poisson statistics, which is indeed true for energies close to the band edges where the quasiparticle obeys the Schrödinger equation.

Cross-section fluctuations in chaotic scattering systems.

Exact analytical expressions for the cross-section correlation functions of chaotic scattering systems have hitherto been derived only under special conditions. The objective of the present article is to provide expressions that are applicable beyond these restrictions. The derivation is based on a statistical model of Breit-Wigner type for chaotic scattering amplitudes which has been shown to describe the exact analytical results for the scattering (S)-matrix correlation functions accurately.

Long-range correlations in rectangular cavities containing pointlike perturbations.

We investigated experimentally the short- and long-range correlations in the fluctuations of the resonance frequencies of flat, rectangular microwave cavities that contained antennas acting as pointlike perturbations. We demonstrate that their spectral properties exhibit the features typical for singular statistics. Hitherto, only the nearest-neighbor spacing distribution had been studied.

Power Spectrum Analysis and Missing Level Statistics of Microwave Graphs with Violated Time Reversal Invariance.

We present experimental studies of the power spectrum and other fluctuation properties in the spectra of microwave networks simulating chaotic quantum graphs with violated time reversal invariance. On the basis of our data sets, we demonstrate that the power spectrum in combination with other long-range and also short-range spectral fluctuations provides a powerful tool for the identification of the symmetries and the determination of the fraction of missing levels. Such a procedure is indispensable for the evaluation of the fluctuation properties in the spectra of real physical systems like, e.