The cat maps: quantum mechanics and classical motion
The cat maps: quantum mechanics and classical motion
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猫图：量子力学和经典运动
DOI：
10.1088/0951-7715/4/2/006
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发表时间：
1991
期刊：
影响因子：
1.7
通讯作者：
J. Keating
中科院分区：
文献类型：
--
作者：
J. Keating
研究了单位2环面的双曲自同构与量子自同构之间的关系。根据经典运动的周期轨道，导出了态的量子密度的精确和显式表示。然后，这被用来获得量子传播子本征值分布的某些统计的精确公式。结果表明，这些统计量强烈地依赖于无量纲普朗克常数的算术性质。作者研究了它们的半经典形式，并利用关于长周期轨道分布的结果，发现它们与以前研究的普适性类中的任何一个都不对应。最后，导出了量子本征函数的性质与周期轨道之间的关系公式。
The relationship between the hyperbolic automorphisms of the unit 2-torus and their quantum counterparts is studied. An exact and explicit representation of the quantum density of states in terms of the periodic orbits of the classical motion is derived. This is then used to obtain exact formulae for certain statistics of the distribution of the eigenvalues of the quantum propagator. It is shown that these statistics are strongly dependent upon the arithmetical nature of the dimensionless Planck's constant. The authors investigate their semiclassical form and, using results concerning the distribution of the long period orbits, find that they do not correspond to those of any of the universality classes previously studied. Finally, formulae are derived which relate properties of the quantum eigenfunctions to the periodic orbits.