Distributions of the Wigner reaction matrix for microwave networks with symplectic symmetry in the presence of absorption

TL;DR

This study experimentally investigates the distribution of the Wigner reaction matrix in microwave networks with symplectic symmetry, comparing results to random matrix theory predictions and Monte Carlo simulations, across different absorption levels.

Contribution

It provides the first experimental validation of RMT predictions for the Wigner reaction matrix in symplectic microwave networks with absorption, confirming theoretical and simulation results.

Findings

Experimental results agree with RMT predictions for reflection coefficients and K matrix distributions.

Absorption influences the distributions but deviations from RMT are minimal.

Nonuniversal effects in spectral properties do not affect open system matrix distributions.

Abstract

We report on experimental studies of the distribution of the reflection coefficients, and the imaginary and real parts of Wigner's reaction (K) matrix employing open microwave networks with symplectic symmetry and varying size of absorption. The results are compared to analytical predictions derived for the single-channel scattering case within the framework of random matrix theory (RMT). Furthermore, we performed Monte Carlo simulations based on the Heidelberg approach for the scattering (S) and K matrix of open quantum-chaotic systems and the two-point correlation function of the S-matrix elements. The analytical results and the Monte Carlo simulations depend on the size of absorption. To verify them, we performed experiments with microwave networks for various absorption strengths. We show that deviations from RMT predictions observed in the spectral properties of the corresponding closed quantum graph, and attributed to the presence of nonuniversal short periodic orbits, does not have any visible effects on the distributions of the reflection coefficients and the K and S matrices associated with the corresponding open quantum graph.