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Spectral correlations of individual quantum graphs

Sven Gnutzmann·Alexander Altland
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Abstract

We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the `energy'--average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric non--linear $σ$--model action. This proves that spectral correlations of individual quantum graphs behave according to the predictions of Wigner--Dyson random matrix theory. We explore the stability of the universal random matrix behavior with regard to perturbations, and discuss the crossover between different types of symmetries.

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Sven Gnutzmann, Alexander Altland. 2005-08-03. Spectral correlations of individual quantum graphs. https://doi.org/10.1103/physreve.72.056215

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