ABSTRACT
This chapter demonstrates that using a simple experimental setup consisting of microwave networks, one may successfully simulate quantum graphs. Quantum graphs are often used as idealizations of physical networks in the limit where the widths of the wires are much smaller than their lengths, assuming that the propagating waves remain in a single transversal mode. The analogy between quantum graphs and microwave networks is based on the equivalency of the Schrodinger equation describing a quantum system and the telegraph equation describing an ideal microwave circuit. In the case of two dimensions, the Schrödinger equation for quantum billiards is equivalent to the Helmholtz equation for microwave cavities of corresponding shape. The experimentally measured fully connected hexagon networks were described in numerical calculations by fully connected quantum hexagon graphs with one lead attached to the 6-joint vertex. The microwave networks with broken time reversal symmetry were constructed using microwave circulators.
