圆台球中的闭合轨道和空间密度振荡
Closed orbits and spatial density oscillations in the circular billiard
摘要：
我们提出了一个案例研究的粒子和动能密度的振荡的二维圆形台球的半经典计算。对于这个系统，我们可以给出所有闭周期和非周期轨道的完整分类。我们讨论了它们的分歧下的变化的起点r，并推导出解析表达式的性质，如行动，稳定性决定因素，动量失配和Morse指数。我们使用最近开发的闭合轨道理论[Roccia J和Brack M 2008 Phys.Rev.Lett. 100 200408]，采用标准的一致近似扰动和分歧理论，并测试收敛的闭轨道总和。
英文摘要：
We present a case study for the semiclassical calculation of the oscillations in the particle and kinetic-energy densities for the two-dimensional circular billiard. For this system, we can give a complete classification of all closed periodic and non-periodic orbits. We discuss their bifurcations under variation of the starting point r and derive analytical expressions for their properties such as actions, stability determinants, momentum mismatches and Morse indices. We present semiclassical calculations of the spatial density oscillations using a recently developed closed-orbit theory [Roccia J and Brack M 2008 Phys. Rev. Lett. 100 200408], employing standard uniform approximations from perturbation and bifurcation theory, and test the convergence of the closed-orbit sum.
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