Ergodic properties of quantized toral automorphisms

Details Ergodic properties of quantized toral automorphisms Ergodic properties of quantized toral automorphisms

1995-12-08

arxiv.org/abs/chao-dyn/9512003v1

Nonlinear Sciences

Chaotic Dynamics

21 pages, plain Tex

Scientific paper

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].

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