Parabolic maps with spin: generic spectral statistics with non-mixing classical limit (Q2782715)
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scientific article; zbMATH DE number 1725404
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Parabolic maps with spin: generic spectral statistics with non-mixing classical limit |
scientific article; zbMATH DE number 1725404 |
Statements
Parabolic maps with spin: generic spectral statistics with non-mixing classical limit (English)
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8 April 2002
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spin 1/2
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random matrix theory
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spectral statistics
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ergodic map
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mixing map
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integrable map
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The paper provides an example of quantum systems with generic spectral statistics (in the sense of random matrix theory), which have however non-mixing classical limits. The construction is based on ergodic but not mixing classic maps of the torus. Their quantised analogues do not have generic spectral statistics, however a coupling to a spin 1/2 changes their behaviour. This was established by a numeric observation. Authors discuss the analogous situation for an almost-integrable map.
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