Spectral correlations of individual quantum graphs

Journal Article · Tue Nov 01 00:00:00 EST 2005 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.72.056215· OSTI ID:20709843

Gnutzmann, Sven; Altland, Alexander ^[1]

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1. Institut fuer Theoretische Physik, Freie Universitaet Berlin, Arnimallee 14, 14195 Berlin (Germany) and Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100 (Israel)

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 nonlinear {sigma}-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.

• OSTI ID: 20709843
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 72, Issue 5; Other Information: DOI: 10.1103/PhysRevE.72.056215; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
CHAOS THEORY
CORRELATIONS
DISTURBANCES
GRAPH THEORY
NONLINEAR PROBLEMS
RANDOMNESS
SIGMA MODEL
SUPERSYMMETRY