PMID: 15244917Jul 13, 2004Paper

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

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Sven Gnutzmann, Burkhard Seif

Abstract

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.

References

Feb 15, 1993·Physical Review. B, Condensed Matter·N ArgamanU Smilansky
Dec 27, 1993·Physical Review Letters·N ArgamanU Smilansky
Dec 11, 1995·Physical Review Letters·O AgamA V Andreev
Aug 19, 1996·Physical Review Letters·E B Bogomolny, J P Keating
Mar 23, 2002·Physical Review Letters·Gregory BerkolaikoRobert S Whitney
Jun 6, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sven GnutzmannMartin R Zirnbauer

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Citations

Dec 31, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sebastian MüllerAlexander Altland
Dec 31, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sven Gnutzmann, Alexander Altland
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yu Dabaghian
Dec 17, 2004·Physical Review Letters·Sven Gnutzmann, Alexander Altland

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