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Title: Spectral fluctuations of quantum graphs

We prove the Bohigas-Giannoni-Schmit conjecture in its most general form for completely connected simple graphs with incommensurate bond lengths. We show that for graphs that are classically mixing (i.e., graphs for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap), the generating functions for all (P,Q) correlation functions for both closed and open graphs coincide (in the limit of infinite graph size) with the corresponding expressions of random-matrix theory, both for orthogonal and for unitary symmetry.
Authors:
 [1] ;  [2]
  1. Faculty of Mathematics and Physics, Charles University, 180 00 Praha 8 (Czech Republic)
  2. Max-Planck-Institut für Kernphysik, 69029 Heidelberg (Germany)
Publication Date:
OSTI Identifier:
22307979
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1619; Journal Issue: 1; Conference: 4. conference on nuclei and mesoscopic physics 2014, East Lansing, MI (United States), 5-9 May 2014; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOND LENGTHS; CORRELATION FUNCTIONS; DIAGRAMS; FLUCTUATIONS; GRAPH THEORY; MATHEMATICAL OPERATORS; MATHEMATICAL SOLUTIONS; MATRICES; MIXING; QUANTUM MECHANICS; RANDOMNESS; UNITARY SYMMETRY