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arxiv: nlin/0312061 · v1 · submitted 2003-12-23 · 🌊 nlin.CD

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Quantum and Arithmetical Chaos

Eugene Bogomolny
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classification 🌊 nlin.CD
keywords chaosquantumlecturesapplicationsarithmeticalaroundcenteredcorrelation
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The lectures are centered around three selected topics of quantum chaos: the Selberg trace formula, the two-point spectral correlation functions of Riemann zeta function zeros, and of the Laplace--Beltrami operator for the modular group. The lectures cover a wide range of quantum chaos applications and can serve as a non-formal introduction to mathematical methods of quantum chaos.

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    Equidistribution of Hecke operators in large N CFT limits reduces the partition function to light-state Poincaré series with an immediate interpretation as sums over handlebody geometries.