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Spectral correlations of individual quantum graphs

Presented by: 
S Gnutzmann [Nottingham]
Tuesday 3rd April 2007 - 14:00 to 15:00
INI Seminar Room 1

The spectral correlations of large well-connected quantum graphs are shown to behave according to the predictions of random-matrix theory by using a supersymmentry method. In a first (generally applicable) step the energy-average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric nonlinear sigma-model action. Reducing the full sigma-model to its mean field theory is equivalent to the random-matrix theory of the Wigner-Dyson ensembles. Conditions for the validity of a mean field description will be discussed along with the stability of the universal random matrix behavior with regard to perturbations.

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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons