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Title: Spectral correlations of individual quantum graphs

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 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.

Authors:
;  [1];  [2]
  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)
  2. (Germany)
Publication Date:
OSTI Identifier:
20709843
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevE.72.056215; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; CHAOS THEORY; CORRELATIONS; DISTURBANCES; GRAPH THEORY; NONLINEAR PROBLEMS; RANDOMNESS; SIGMA MODEL; SUPERSYMMETRY

Citation Formats

Gnutzmann, Sven, Altland, Alexander, and Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Cologne. Spectral correlations of individual quantum graphs. United States: N. p., 2005. Web. doi:10.1103/PhysRevE.72.056215.
Gnutzmann, Sven, Altland, Alexander, & Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Cologne. Spectral correlations of individual quantum graphs. United States. doi:10.1103/PhysRevE.72.056215.
Gnutzmann, Sven, Altland, Alexander, and Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Cologne. Tue . "Spectral correlations of individual quantum graphs". United States. doi:10.1103/PhysRevE.72.056215.
@article{osti_20709843,
title = {Spectral correlations of individual quantum graphs},
author = {Gnutzmann, Sven and Altland, Alexander and Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Cologne},
abstractNote = {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.},
doi = {10.1103/PhysRevE.72.056215},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
number = 5,
volume = 72,
place = {United States},
year = {Tue Nov 01 00:00:00 EST 2005},
month = {Tue Nov 01 00:00:00 EST 2005}
}