Quantum-classical correspondences of the Berry-Robnik parameter through bifurcations in lemon billiard systems.
Quantum-classical correspondences of the Berry-Robnik parameter through bifurcations in lemon billiard systems.
复制标题
柠檬台球系统中分叉的 Berry-Robnik 参数的量子经典对应关系。
DOI：
--
复制
发表时间：
2001
期刊：
影响因子：
--
通讯作者：
Yoji Aizawa
中科院分区：
文献类型：
--
作者：
H. Makino;Takahisa Harayama;Yoji Aizawa
利用一类单参数柠檬台球系统研究了经典动力学中分支对量子能级统计的影响。我们系统的经典相空间由规则和不规则区域组成。我们确定了这些地区的相体积作为系统参数的函数的解析解，并表明该函数揭示了尖点奇点的分歧点。该功能相比，其量子力学对应的贝里-Robnik参数。通过估计半经典制度的有效普朗克常数，验证量子经典对应的贝里-Robnik参数，我们确定了一个区域的系统参数的尖点可以再现的统计特性的本征能级。
The quantum level statistics affected by bifurcations in classical dynamics is studied by using a one-parameter family of lemon billiard systems. The classical phase space of our system consists of regular and irregular regions. We determine an analytic solution of the phase volume for these regions as a function of the system parameter and show that the function reveals a cusp singularity at the bifurcation point. The function is compared with its quantum mechanical counterpart, the Berry-Robnik parameter. By estimating the semiclassical regime from the effective Planck constant that validates the quantum-classical correspondence of the Berry-Robnik parameter, we determine a region of the system parameter where the cusp can be reproduced by the statistical properties of the eigenenergy levels.