- 96-52 Klimek S., Lesniewski A., Maitra N., Rubin R.
- Ergodic properties of quantized toral automorphisms
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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 . 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 .