Arnd Bäcker and Grischa Haag 1999 J. Phys. A: Math. Gen. 32 L393 doi:10.1088/0305-4470/32/36/101
Spectral statistics for quantized skew translations on the torus
Arnd Bäcker and Grischa Haag
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We study the spectral statistics for quantized skew translations on the torus, which are ergodic but not mixing for irrational parameters. It is shown explicitly that in this case the level-spacing distribution and other common spectral statistics, like the number variance, do not exist in the semiclassical limit.
- PACS
- MSC
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81Q20 Semiclassical techniques including WKB and Maslov methods
81R12 Relations with integrable systems (See also 17Bxx, 37J35)
- Subjects
- Dates
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Issue 36 (10 September 1999)
Received 7 May 1999, in final form 5 July 1999
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Spectral statistics for quantized skew translations on the torus
Arnd Bäcker and Grischa Haag 1999 J. Phys. A: Math. Gen. 32 L393
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