Spectral statistics and periodic orbits (Q2760019)
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scientific article; zbMATH DE number 1683989
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Spectral statistics and periodic orbits |
scientific article; zbMATH DE number 1683989 |
Statements
18 December 2001
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random matrices
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quantum eigenvalues for chaotic systems
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semiclassical trace formulas
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spectral statistics
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Gaussian unitary ensemble
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zeros
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Riemann zeta-function
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Spectral statistics and periodic orbits (English)
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The goal of this paper is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semiclassical trace formulas. Under the assumption that periodic orbit actions are noncommonsurable, the author shows that the spectral statistics of the chaotic systems without time reversal invariance in the universal limit agrees with statistics of the Gaussian unitary ensemble of random matrices. The author also discusses in detail the statistics of the zeros of the Riemann zeta-function.NEWLINENEWLINEFor the entire collection see [Zbl 0972.00065].
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