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Quantum graphs: II. Some spectral properties of quantum and combinatorial graphs

✍ Scribed by Kuchment, Peter

Book ID
115503629
Publisher
Institute of Physics
Year
2005
Tongue
English
Weight
160 KB
Volume
38
Category
Article
ISSN
0305-4470

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We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also define a classical phase space for the graphs, where the dynamics is mixing and the periodic orbits