关于量子李雅普诺夫指数的概念
On the notion of quantum Lyapunov exponent
摘要：
经典混沌是指当时间趋于无穷大时，轨道呈指数发散的特性。它的特征是一个积极的李雅普诺夫指数。量子混沌有许多不同的描述。与广义（量子）李雅普诺夫指数的概念相关的一个是基于定性物理考虑或所谓的辛层析成像映射。本文的目的是说明量子李雅普诺夫指数的定义是如何在量子力学的Moyal相空间公式的框架中自然产生的，并且是基于量子轨道和量子化子族的概念。明确了海森堡不确定原理在量子混沌判据陈述中的作用。
英文摘要：
Classical chaos refers to the property of trajectories to diverge exponentially as time tends to infinity. It is characterized by a positive Lyapunov exponent. There are many different descriptions of quantum chaos. The one related to the notion of generalized (quantum) Lyapunov exponent is based either on qualitative physical considerations or on the so-called symplectic tomography map. The purpose of this note is to show how the definition of quantum Lyapunov exponent naturally arises in the framework of the Moyal phase space formulation of quantum mechanics and is based on the notions of quantum trajectories and the family of quantizers. The role of the Heisenberg uncertainty principle in the statement of the criteria for quantum chaos is made explicit.
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