Universal spectral statistics in Wigner-Dyson, chiral and Andreev star graphs II: semiclassical approach

Details Universal spectral statistics in Wigner-Dyson, chiral and Andreev star graphs II: semiclassical approach Universal spectral statistics in Wigner-Dyson, chiral and Andreev star graphs II: semiclassical approach

2003-09-18

arxiv.org/abs/nlin/0309050v1

Nonlinear Sciences

Chaotic Dynamics

15 Pages

Scientific paper

10.1103/PhysRevE.69.056220

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 upto 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.

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