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arXiv quant-ph/0205148quant-ph
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量子敏感依赖

Quantum sensitive dependence

V. I. Man'ko, R. Vilela Mendes

摘要:

具有与时间无关势的有界量子系统的波函数是概周期函数,不可能像经典混沌那样具有时间渐近性。然而,在量子控制中使用的具有依赖于时间的相互作用的有界量子系统可能具有连续谱,并且可观测量的增长率是理论和实际关注的问题。在量子力学的增长率进行了讨论,通过构建与经典的李雅普诺夫指数中所涉及的物理意义相同的量。量子敏感依赖的广义概念的介绍和数学结构的运营商矩阵元素,对应于不同类型的增长的特点。

英文摘要:

Wave functions of bounded quantum systems with time-independent potentials, being almost periodic functions, cannot have time asymptotics as in classical chaos. However, bounded quantum systems with time-dependent interactions, as used in quantum control, may have continuous spectrum and the rate of growth of observables is an issue of both theoretical and practical concern. Rates of growth in quantum mechanics are discussed by constructing quantities with the same physical meaning as those involved in the classical Lyapunov exponent. A generalized notion of quantum sensitive dependence is introduced and the mathematical structure of the operator matrix elements that correspond to different types of growth is characterized.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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