Experimental study of the distributions of off-diagonal scattering-matrix elements of quantum graphs with symplectic symmetry

TL;DR

This study experimentally investigates the distribution of off-diagonal scattering matrix elements in quantum graphs with symplectic symmetry, comparing results to random-matrix theory and analyzing deviations due to subgraph connectivity.

Contribution

It provides experimental data on symplectic quantum graphs and compares these to theoretical predictions, highlighting the impact of subgraph connectivity on scattering matrix distributions.

Findings

Distributions align with random-matrix theory predictions under ideal conditions.

Deviations occur when subgraphs are not fully connected.

Connectivity influences scattering matrix element distributions.

Abstract

We report on experimental studies of the distribution of the off-diagonal elements of the scattering matrix of open microwave networks with symplectic symmetry and a chaotic wave dynamics. These consist of two geometrically identical subgraphs with unitary symmetry described by complex conjugate Hamiltonians, that are coupled by a pair of bonds. The results are compared to random-matrix theory predictions obtained on the basis of the Heidelberg approach for the scattering matrix of open quantum-chaotic systems. We demonstrate that deviations from random-matrix theory predictions observed in the distributions may be attributed to the fact that the subgraphs are not fully connected.