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arXiv · 0903.3136

Experimental and numerical investigation of the reflection coefficient and the distributions of Wigner's reaction matrix for irregular graphs with absorption

Michal Lawniczak·Oleh Hul·Szymon Bauch·Petr Seba·Leszek Sirko
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Abstract

We present the results of experimental and numerical study of the distribution of the reflection coefficient P(R) and the distributions of the imaginary P(v) and the real P(u) parts of the Wigner's reaction K matrix for irregular fully connected hexagon networks (graphs) in the presence of strong absorption. In the experiment we used microwave networks, which were built of coaxial cables and attenuators connected by joints. In the numerical calculations experimental networks were described by quantum fully connected hexagon graphs. The presence of absorption introduced by attenuators was modelled by optical potentials. The distribution of the reflection coefficient P(R) and the distributions of the reaction K matrix were obtained from the measurements and numerical calculations of the scattering matrix S of the networks and graphs, respectively. We show that the experimental and numerical results are in good agreement with the exact analytic ones obtained within the framework of random matrix theory (RMT).

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Michal Lawniczak, Oleh Hul, Szymon Bauch, Petr Seba, Leszek Sirko. 2009-03-18. Experimental and numerical investigation of the reflection coefficient and the distributions of Wigner's reaction matrix for irregular graphs with absorption. https://doi.org/10.1103/physreve.77.056210

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