Spectral fluctuations of quantum graphs

Journal Article · Wed Oct 15 00:00:00 EDT 2014 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.4899227· OSTI ID:22307979

Pluhař, Z. ^[1]; Weidenmüller, H. A. ^[2]

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1. Faculty of Mathematics and Physics, Charles University, 180 00 Praha 8 (Czech Republic)
2. Max-Planck-Institut für Kernphysik, 69029 Heidelberg (Germany)

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.

• OSTI ID: 22307979
• Journal Information: AIP Conference Proceedings, Vol. 1619, 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); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

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