Experimental investigation of Wigner's reaction matrix for irregular graphs with absorption

TL;DR

This paper experimentally investigates the Wigner's reaction matrix in irregular microwave networks with absorption, comparing measurements with theoretical predictions to validate models of wave scattering in complex systems.

Contribution

It provides the first experimental validation of the Wigner's reaction matrix distributions in irregular graphs with absorption using microwave networks.

Findings

Measured distributions match theoretical predictions

Good agreement between experimental data and models

Validated the use of microwave networks as analogs for irregular graphs

Abstract

We use tetrahedral microwave networks consisting of coaxial cables and attenuators connected by T-joints to make an experimental study of Wigner's reaction K matrix for irregular graphs in the presence of absorption. From measurements of the scattering matrix S for each realization of the microwave network we obtain distributions of the imaginary and real parts of K. Our experimental results are in good agreement with theoretical predictions.