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Spectral statistics for quantized skew translations on the torus

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, , Citation Arnd Bäcker and Grischa Haag 1999 J. Phys. A: Math. Gen. 32 L393 DOI 10.1088/0305-4470/32/36/101

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1 Abteilung Theoretische Physik, Universität Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Federal Republic of Germany

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  1. Received 7 May 1999

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0305-4470/32/36/L393

Abstract

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.

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