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

TL;DR

This study combines experimental and numerical methods to analyze the reflection coefficient and Wigner's reaction matrix distributions in irregular graphs with absorption, confirming results with random matrix theory.

Contribution

It provides the first comprehensive comparison of experimental, numerical, and theoretical distributions of scattering matrices in irregular graphs with absorption.

Findings

Experimental and numerical results agree with theoretical predictions.

Absorption significantly affects the distribution of the reflection coefficient.

Distributions match those derived from random matrix theory.

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).