Experimental investigation of the enhancement factor for irregular undirected and directed microwave graphs

Quantum graphs are widely used to investigate properties of quantum chaos. Experimentally, quantum graphs are simulated by microwave graphs (networks) consisting of joints, microwave cables and other microwave components such as attenuators and circulators. This is possible due to an equivalency of the one-dimensional Schrödinger equation describing a quantum system and the telegraph equation describing an ideal microwave network. We present the results of the experimental study of the enhancement factor W_s,β for irregular fully connected hexagon undirected and directed microwave graphs in the presence of absorption. We measured the two-port scattering matrix Ŝ for the undirected microwave graphs which statistical properties of eigenfrequencies, typical for the systems with time reversal symmetry (TRS), can be described by Gaussian Orthogonal Ensemble (GOE) in Random Matrix Theory (RMT), and for the directed graphs possessing the properties of the systems with broken time reversal symmetry, which can be described by Gaussian Unitary Ensemble (GUE) in RMT. The measurements were performed as a function of absorption, which was varied by microwave attenuators.