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

We report on experimental studies of the distribution of the off-diagonal elements of the scattering (S) matrix of open microwave networks with symplectic symmetry and 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 (RMT) predictions obtained on the basis of the Heidelberg approach for the S matrix of open quantum-chaotic systems, employing random matrices from the Gaussian symplectic ensemble. We demonstrate that deviations observed in the distributions of the off-diagonal S-matrix elements may be attributed to the fact that the subgraphs are not fully connected, and propose a RMT model, which takes this into account and indeed confirms the experimental results.