Universal spectral statistics in Wigner-Dyson, chiral, and Andreev star graphs. II. Semiclassical approach

A semiclassical approach to the universal ergodic spectral statistics in quantum star graphs is presented for all known ten symmetry classes of quantum systems. The approach is based on periodic orbit theory, the exact semiclassical trace formula for star graphs, and on diagrammatic techniques. The appropriate spectral form factors are calculated up to one order beyond the diagonal and self-dual approximations. The results are in accordance with the corresponding random-matrix theories which supports a properly generalized Bohigas-Giannoni-Schmit conjecture.