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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 156, Number 1, Pages 38–66
DOI: https://doi.org/10.4213/tmf6229 (Mi tmf6229) 		 
Analytic description of statistics of spectra of quantum graphs

Yu. A. Dabaghian

University of California, San Francisco
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DOI: https://doi.org/10.4213/tmf6229
Abstract: 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.
Keywords: quantum chaos, spectral theory, universal distribution, almost independent random variable, analytic method.
Received: 30.05.2007
English version:
Theoretical and Mathematical Physics, 2008, Volume 156, Issue 1, Pages 996–1019
DOI: https://doi.org/10.1007/s11232-008-0094-8
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Language: Russian
Citation: Yu. A. Dabaghian, “Analytic description of statistics of spectra of quantum graphs”, TMF, 156:1 (2008), 38–66; Theoret. and Math. Phys., 156:1 (2008), 996–1019
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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