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We present the results of experimental and theoretical study of irregular,tetrahedral microwave networks consisting of coaxial cables (annularwaveguides) connected by T-joints. The spectra of the networks were measured inthe frequency range 0.0001-16 GHz in order to obtain their statisticalproperties such as the integrated nearest neighbor spacing distribution and thespectral rigidity. The comparison of our experimental and theoretical resultsshows that microwave networks can simulate quantum graphs with time reversalsymmetry. In particular, we use the spectra of the microwave networks to studythe periodic orbits of the simulated quantum graphs. We also presentexperimental study of directional microwave networks consisting of coaxialcables and Faraday isolators for which the time reversal symmetry is broken. Inthis case our experimental results indicate that spectral statistics ofdirectional microwave networks deviate from predictions of Gaussian orthogonalensembles (GOE) in random matrix theory approaching, especially for smalleigenfrequency spacing s, results for Gaussian unitary ensembles (GUE).Experimental results are supported by the theoretical analysis of directionalgraphs.Comment: 16 pages, 7 figures, to be published in Phys. Rev.

Experimental simulation of quantum graphs by microwave networks