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We present the results of experimental and numerical study of thedistribution of the reflection coefficient P(R) and the distributions of theimaginary P(v) and the real P(u) parts of the Wigner's reaction K matrix forirregular fully connected hexagon networks (graphs) in the presence of strongabsorption. In the experiment we used microwave networks, which were built ofcoaxial cables and attenuators connected by joints. In the numericalcalculations experimental networks were described by quantum fully connectedhexagon graphs. The presence of absorption introduced by attenuators wasmodelled by optical potentials. The distribution of the reflection coefficientP(R) and the distributions of the reaction K matrix were obtained from themeasurements and numerical calculations of the scattering matrix S of thenetworks and graphs, respectively. We show that the experimental and numericalresults are in good agreement with the exact analytic ones obtained within theframework of random matrix theory (RMT).

physical review. e, statistical, nonlinear and soft matter physics

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