Oleh Hul

Experimental investigation of Wigner's reaction matrix for irregular graphs with absorption

We use tetrahedral microwave networks consisting of coaxial cables and attenuators connected by T-joints to make an experimental study of Wigners reaction K matrix for irregular graphs in the presence of absorption. From measurements of the scattering matrix S for each realization of the microwave network, we obtain distributions of the imaginary and real parts of K. Our experimental results are in good agreement with theoretical predictions.

Experimental investigation of properties of hexagon networks with and without time reversal symmetry

We present the results of experimental study of the distribution P(R) of the reflection coefficient R and the distributions of Wigners reaction K matrix for irregular hexagon fully connected microwave networks simulating quantum graphs with time reversal symmetry (TRS) in the presence of absorption. The distributions of the reflection coefficient R and the real and imaginary parts of K matrix were obtained from the measurements of the scattering matrix S of the microwave networks. Furthermore, we show that the microwave networks with microwave circulators can be used to study systems with broken TRS. Properties of such networks are investigated using the cross-correlation function c12(ν) and the integrated nearest-neighbor spacing distribution I(s).

Experimental investigation of microwave networks simulating quantum chaotic systems: the role of direct processes

The influence of direct processes on the cross-correlation function c12(ν) and the elastic enhancement factor WS, β was studied experimentally using microwave networks in the presence of absorption. Microwave networks simulate quantum graphs with and without time-reversal symmetry. Direct processes exist because, for example, of non-perfect coupling between a studied system and a measuring device. We show that direct processes strongly influence the cross-correlation function c12(ν) in contrast to the enhancement factor WS, β, which is not sensitive to these processes. It makes the enhancement factor WS, β an important measure of the chaoticity of a quantum system.

Experimental investigation of the enhancement factor and the cross-correlation function for graphs with and without time-reversal symmetry: the open system case

We present the results of an experimental study of the enhancement factor WS,? of the two-port scattering matrix and the cross-correlation function c12(?) for microwave irregular networks simulating quantum graphs with time-reversal symmetry (TRS), symmetry index ?=1, and without TRS, ?=2, in the presence of absorption. We show that even for systems with notable losses the elastic enhancement factor WS,? remains a statistical measure that allows the determination of a symmetry class of the chaotic quantum systems under investigation. Therefore, the enhancement factor WS,? may be contrasted with many others statistical measures such as, for example, the nearest neighbor spacing distribution or the spectral rigidity, which are not directly applicable in the presence of strong absorption. The quantum graphs with TRS were simulated by the microwave networks built of coaxial cables connected by joints and attenuators, which allowed us to control absorption. The microwave circulators were added to the networks to simulate graphs with broken TRS. The experimental results are compared to the ones obtained within the framework of random matrix theory.

Investigation of parameter-dependent properties of quantum graphs with and without time-reversal symmetry

Parameter-dependent statistical properties of spectra of irregular quantum graphs with and without time-reversal symmetry are studied. The autocorrelation functions of level velocities and as well as the distribution of avoided crossing gaps are calculated. The numerical results are compared with the predictions of random matrix theory (RMT).

Experimental and numerical determination of the correlation function of level velocities for microwave networks simulating quantum graphs

The parameter-dependent correlation function of level velocities is studied experimentally and numerically. The measurements were made for microwave networks simulating quantum graphs. One- and two-port measurements of the scattering matrix necessary for determining the correlation function were realized for the five vertices networks. For the fully connected six vertices network, one-port measurements were made. The obtained experimental and numerical results are compared with the predictions of random matrix theory.

Experimental investigation of the enhancement factor for irregular undirected and directed microwave graphs

Quantum graphs are widely used to investigate properties of quantum chaos. Experimentally, quantum graphs are simulated by microwave graphs (networks) consisting of joints, microwave cables and other microwave components such as attenuators and circulators. This is possible due to an equivalency of the one!dimensional Schrodinger equation describing a quantum system and the telegraph equation describing an ideal microwave network. We present the results of the experimental study of the enhancement factor WS, β for irregular fully connected hexagon undirected and directed microwave graphs in the presence of absorption. We measured the two!port scattering matrix Ŝ for the undirected microwave graphs which statistical properties of eigenfrequencies, typical for the systems with time reversal symmetry (TRS), can be described by Gaussian Orthogonal Ensemble (GOE) in Random Matrix Theory (RMT), and for the directed graphs possessing the properties of the systems with broken time reversal symmetry, which can be described by Gaussian Unitary Ensemble (GUE) in RMT. The measurements were performed as a function of absorption, which was varied by