The quantum Bernoulli map

Details The quantum Bernoulli map The quantum Bernoulli map

2011-10-24

arxiv.org/abs/1110.5122v1

Physics

Quantum Physics

22 pages, 7 figures. Submitted to Bussei Kenkyu, special volume honoring S. Tasaki

Scientific paper

The classical Bernoulli and baker maps are two simple models of deterministic chaos. On the level of ensembles, it has been shown that the time evolution operator for these maps admits generalized spectral representations in terms of decaying eigenfunctions. We introduce the quantum version of the Bernoulli map. We define it as a projection of the quantum baker map. We construct a quantum analogue of the generalized spectral representation, yielding quantum decaying states represented by density matrices. The quantum decaying states develop a quasi-fractal shape limited by the quantum uncertainty.

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