运动近似积分与量子混沌问题
Approximate integrals of motion and the quantum chaoticity problem
摘要：
讨论了定态量子力学中运动积分的存在性和构造问题及其与量子混沌性的关系。结果表明，较早提出的量子混沌性判据表征了正则系统初始对称性的破坏和基量子数在微扰影响下的破坏。建议的收敛过程，允许构造近似积分的运动的非平凡组合的形式取决于运营商$(q,p)$。讨论了所得到的具有复杂结构的积分的性质及其存在性对系统动力学的影响。该方法用于显式构造和研究Henon-Heiles问题的近似积分。
英文摘要：
The problem of existence and constructing of integrals of motion in stationary quantum mechanics and its connection with quantum chaoticity is discussed. It is shown that the earlier suggested quantum chaoticity criterion characterizes destruction of initial symmetry of regular system and of basis quantum numbers under influence of perturbation. The convergent procedure allowing to construct approximate integrals of motion in the form of non-trivial combinations depending on operators $(q,p)$ is suggested. Properties of the obtained integrals with complicated structure and the consequences of their existence for system's dynamics are discussed. The method is used for explicit construction and investigation of the approximate integrals in Henon-Heiles problem.
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