Experimental simulation of quantum graphs by microwave networks.

  title={Experimental simulation of quantum graphs by microwave networks.},
  author={Oleh Hul and Szymon Bauch and Prot Pakoński and Nazar Savytskyy and Karol Życzkowski and Leszek Sirko},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={69 5 Pt 2},
  • Oleh Hul, S. Bauch, +3 authors L. Sirko
  • Published 2 April 2004
  • Mathematics, Physics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
We present the results of experimental and theoretical study of irregular, tetrahedral microwave networks consisting of coaxial cables (annular waveguides) connected by T joints. The spectra of the networks were measured in the frequency range 0.0001-16 GHz in order to obtain their statistical properties such as the integrated nearest neighbor spacing distribution and the spectral rigidity Delta(3) (L). The comparison of our experimental and theoretical results shows that microwave networks can… Expand
Experimental Study of Quantum Graphs with Simple Microwave Networks: Non-Universal Features
Quantum graphs provide a setting to test the hypothesis that all ray-chaotic systems show universal wave chaotic properties. Here, an experimental setup consisting of a microwave coaxial cableExpand
Experimental Determination of the Autocorrelation Function of Level Velocities for Microwave Networks Simulating Quantum Graphs
The autocorrelation function c(x) of level velocities is studied experimentally. The measurements were performed for microwave networks simulating quantum graphs. One and two ports measurements ofExpand
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 Wigner's reaction K matrix for irregular hexagon fully connectedExpand
Experimental investigation of the enhancement factor for microwave irregular networks with preserved and broken time reversal symmetry in the presence of absorption.
It is shown that the experimental results obtained for networks with moderate and strong absorption are in good agreement with the ones obtained within the framework of random matrix theory. Expand
Spectral duality in graphs and microwave networks.
The graph spectrum is obtained from the zeros of a secular determinant derived from energy and charge conservation, with the consequence that the Neumann spectrum is described by random matrix theory only locally, but adopts features of the interlacing Dirichlet spectrum for long-range correlations. Expand
Experimental and numerical investigation of the reflection coefficient and the distributions of Wigner's reaction matrix for irregular graphs with absorption.
An experimental and numerical study of the distribution of the reflection coefficient P(R) and the distributions of the imaginary and real parts of the Wigner reaction K matrix for irregular fully connected hexagon networks (graphs) in the presence of strong absorption. Expand
Experimental Investigation of Reflection Coefficient and Wigner's Reaction Matrix for Microwave Graphs
Quantum graphs of connected one-dimensional wires were introduced by Pauling seven decades ago [1]. The same idea was used a decade later by Kuhn [2] to describe organic molecules by free electronExpand
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 simulatingExpand
Spectra and spectral correlations of microwave graphs with symplectic 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. Expand
Are scattering properties of graphs uniquely connected to their shapes?
This work considers scattering from a pair of isospectral microwave networks consisting of vertices connected by microwave coaxial cables and extended to scattering systems by connecting leads to infinity to form isoscattering networks and shows that the amplitudes and phases of the determinants of the scattering matrices of such networks are the same within the experimental uncertainties. Expand


Quantum graphs: a model for quantum chaos
Abstract We study the statistical properties of the scattering matrix associated with generic quantum graphs. The scattering matrix is the quantum analogue of the classical evolution operator on theExpand
Statistical properties of the eigenfrequency distribution of three-dimensional microwave cavities.
  • Deus, Koch, Sirko
  • Physics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1995
It is found that the distribution of electromagnetic eigenmodes of the irregular 3D microwave cavities displays a statistical behavior characteristic for classically chaotic quantum systems, viz., the Wigner distribution, suggesting that it is universal. Expand
Microwave billiards with broken time reversal invariance
We consider a microwave resonator with three single-channel waveguides attached. One of these serves to couple waves into and out of the resonator; the remaining two are connected to form a one-wayExpand
Quantum Chaos on Graphs
We quantize graphs (networks) which consist of a finite number of bonds and nodes. We show that their spectral statistics is well reproduced by random matrix theory. We also define a classical phaseExpand
Periodic Orbit Theory and Spectral Statistics for Quantum Graphs
Abstract We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrixExpand
Dynamical properties of fractal networks: Scaling, numerical simulations, and physical realizations
This article describes the advances that have been made over the past ten years on the problem of fracton excitations in fractal structures. The relevant systems to this subject are so numerous thatExpand
Quantum graphs: a simple model for chaotic scattering
We connect quantum graphs with infinite leads, and turn them into scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlyingExpand
Spectral statistics for unitary transfer matrices of binary graphs
Quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits. It is proposed here to generalize this approachExpand
Wave Chaos Experiments with and without Time Reversal Symmetry: GUE and GOE Statistics.
The first experimental test of the prediction that in the semiclassical regime the level statistics of a classically chaotic system correspond to that of the Gaussian unitary ensemble (GUE) of random matrices when time reversal symmetry is broken is presented. Expand
Experimental test of a trace formula for a chaotic three-dimensional microwave cavity.
We have measured resonance spectra in a superconducting microwave cavity with the shape of a three-dimensional generalized Bunimovich stadium billiard and analyzed their spectral fluctuationExpand