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Analytic description of statistics of spectra of quantum graphs. (English. Russian original) Zbl 1155.81332

Theor. Math. Phys. 156, No. 1, 996-1019 (2008); translation from Teor. Mat. Fiz. 156, No. 1, 38-66 (2008).
Summary: We discuss how to obtain exact and approximate distributions for various statistical characteristics of the spectra of quantum graphs using previously found exact solutions of the spectral problem. We indicate the relation between the appearing spectral decompositions and the theory of weakly dependent random variables and indicate the relation between the known limit theorems for trigonometric sums and the universal statistical properties of the spectra of quantum chaotic systems.

MSC:

81Q50 Quantum chaos
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