Upper Quantum Lyapunov Exponent and Anosov Relations for Quantum Systems Driven by a Classical Flow |
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Authors: | O. Sapin H. R. Jauslin Stefan Weigert |
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Affiliation: | (1) Laboratoire de Physique CNRS - UMR 5027, Université de Bourgogne, BP 47870, F-21078 Dijon, France;(2) Department of Mathematics, University of York, Heslington, YO10 5DD, UK |
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Abstract: | We generalize the definition of quantum Anosov properties and the related Lyapunov exponents to the case of quantum systems driven by a classical flow, i.e. skew-product systems. We show that the skew Anosov properties can be interpreted as regular Anosov properties in an enlarged Hilbert space, in the framework of a generalized Floquet theory. This extension allows us to describe the hyperbolicity properties of almost-periodic quantum parametric oscillators and we show that their upper Lyapunov exponents are positive and equal to the Lyapunov exponent of the corresponding classical parametric oscillators. As second example, we show that the configurational quantum cat system satisfies quantum Anosov properties. |
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Keywords: | quantum dynamics Lyapunov exponents Anosov systems parametric oscillators quantum chaos Arnold’ s cat map |
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