96-52 Klimek S., Lesniewski A., Maitra N., Rubin R.

Ergodic properties of quantized toral automorphisms (48K, plain TeX) Mar 2, 96

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Abstract. 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 [10]. 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, parameterized by the points of a torus, which includes the quantization proposed in [9].

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