Ergodic properties of quantized toral automorphisms

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We study the ergodic properties for a class of quantized toral automorphisms, namely the cat and Kronecker maps. The present work uses and extends the results of [KL]. We show that quantized cat maps are strongly mixing, while Kronecker maps are ergodic and non-mixing. We also study the structure of these quantum maps and show that they are effected by unitary endomorphisms of a suitable vector bundle over a torus. The fiberwise parts of these endomorphisms form a family of finite dimensional quantizations, parametrized by the points of a torus, which includes the quantization proposed in [HB].
21 pages, plain Tex

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Chaotic Dynamics

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http://salesiana.dossiersoluciones.com/handle/123456789/150517

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/chao-dyn/9512003
 http://arxiv.org/abs/chao-dyn/9512003

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arXiv