经典流驱动量子系统的上量子李雅普诺夫指数和Anosov关系
Upper quantum Lyapunov Exponent and Anosov relations for quantum systems driven by a classical flow
摘要：
将量子Anosov性质的定义和相关的李雅普诺夫指数推广到经典流驱动的量子系统，即斜积系统。我们表明，斜Anosov属性可以被解释为经常Anosov属性在扩大的Hilbert空间中，在广义Floquet理论的框架。这种扩展使我们能够描述的双曲性质的准周期量子参量振荡器，我们表明，他们的上李雅普诺夫指数是积极的，等于相应的经典参量振荡器的李雅普诺夫指数。作为第二个例子，我们证明了组态量子猫系统满足量子Anosov性质。
英文摘要：
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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