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Experimental Investigation of Reflection Coefficient and Wigner's Reaction Matrix for Microwave Graphs

100%
Hul O., Bauch S., Ławniczak M., Sirko L.
Acta Physica Polonica A
|
2007
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vol. 112
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issue 4
655-664
EN
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, tetrahedral microwave graphs (networks) in the presence of absorption. Our experimental results are in good agreement with the exact theoretical predictions of Savin et al.
2
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Experimental and Numerical Studies of One-Dimensional and Three-Dimensional Chaotic Open Systems

100%
Ławniczak M., Hul O., Bauch S., Sirko L.
Acta Physica Polonica A
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2009
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vol. 116
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issue 5
749-755
EN
We present the results of experimental studies of microwave irregular networks and a three-dimensional microwave rough cavity in the presence of absorption. Microwave networks are also analyzed numerically. Microwave networks simulate one-dimensional quantum graphs. The networks consist of coaxial cables connected by joints and attenuators to control absorption. Three-dimensional microwave rough cavities have no formal analog in quantum 3D systems. However, some statistical properties of their spectra such as the level spacing distribution confirms that they belong to the wave-chaotic systems. Absorption of the cavity was changed by using a foam microwave absorber.
3
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Experimental Determination of the Autocorrelation Function of Level Velocities for Microwave Networks Simulating Quantum Graphs

88%
Ławniczak M., Borkowska A., Hul O., Bauch S., Sirko L.
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EN
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 of the scattering matrix Ŝ necessary for determining c(x) were realized for the networks possessing 5 and 6 vertices, respectively. The network with six vertices was fully connected. In the case of the networks with five vertices, additionally to the fully connected configuration, we measured the networks without the bond connecting input/output vertices. The obtained experimental results besides the autocorrelation function of level velocities, also the nearest-neighbor spacing distribution and parametric velocities distribution are compared to the predictions of random matrix theory and numerical results.
4
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Nodal Domains in Chaotic Microwave Rough Billiards with and without Ray-Splitting Properties

88%
Hul O., Savytskyy N., Tymoshchuk O., Bauch S., Sirko L.
Acta Physica Polonica A
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2006
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vol. 109
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issue 1
73-87
EN
We study experimentally nodal domains of wave functions (electric field distributions) lying in the regime of Breit-Wigner ergodicity in the chaotic microwave half-circular ray-splitting rough billiard. Using the rough billiard without ray-splitting properties we also study the wave functions lying in the regime of Shnirelman ergodicity. The wave functionsΨ_N of the ray-splitting billiard were measured up to the level number N=204. In the case of the rough billiard without ray-splitting properties, the wave functions were measured up to N=435. We show that in the regime of Breit-Wigner ergodicity most of wave functions are delocalized in the n, l basis. In the regime of Shnirelman ergodicity wave functions are homogeneously distributed over the whole energy surface. For such wave functions, lying both in the regimes of Breit-Wigner and Shnirelman ergodicity, the dependence of the number of nodal domainsƝ_N on the level number N was found. We show that in the regimes of Breit-Wigner and Shnirelman ergodicity least squares fits of the experimental data reveal the numbers of nodal domains that in the asymptotic limit N→∞ coincide within the error limits with the theoretical predictionƝ_N/N≃ 0.062. Finally, we demonstrate that the signed area distributionΣ_A can be used as a useful criterion of quantum chaos.
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