Quantum signatures of chaos
Quantum signatures of chaos
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DOI：
10.1007/978-1-4899-3698-1_38
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发表时间：
1991
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影响因子：
--
通讯作者：
F. Haake
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文献类型：
--
作者：
F. Haake
能级聚类和能级排斥之间的区别是全局规则运动和主要混沌运动之间经典区别的量子类似物之一（见图1、2、3）。为了揭示全局经典混沌条件下的能级排斥，可能需要特别注意：（i）涉及与对称性相关的量子数的不同值的子谱必须单独处理，以及（ii）对于具有量子局域化的系统，仅必须承认其波函数具有重叠支持的能级。在自治系统的情况下，“能级”可以是能量本征值E，或者对于周期性驱动的系统，可以是准能量φ，即从一个周期到另一个周期传输波矢量的酉Floquet算子的本征相。
The distinction between level clustering and level repulsion is one of the quantum analogues of the classical distinction between globally regular and predominantly chaotic motion (see Figs. 1, 2, 3). In order to reveal level repulsion under conditions of global classical chaos special care may be necessary: (i) subspectra referring to different values of the quantum numbers related to symmetries must be dealt with separately and (ii) for systems with quantum localization only levels whose wavefunctions have overlapping support must be admitted. A “level” may either be an energy eigenvalueEin the case of autonomous systems or, for periodically driven systems, a quasi-energyφ, i.e. an eigenphase of the unitary Floquet operator transporting the wavevector from period to period.