Quantum chaos in systems with ray splitting.
Quantum chaos in systems with ray splitting.
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光线分裂系统中的量子混沌。
DOI：
10.1103/physreva.46.6193
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
T. Antonsen
中科院分区：
文献类型：
--
作者：
Luise Couchman;Edward Ott;T. Antonsen
我们考虑这样的波动系统，在这个系统中，光线从尖锐的边界反射而分裂。例如，势能在表面上不连续变化的薛定谔方程，介电常数不连续区域中的电磁波，具有固定或自由边界的弹性介质等。通过引入对射线的蒙特卡罗处理，可以通过标准的Lyapunov数准则来定义混沌射线。以弹性介质为例，对蒙特卡罗射线方法进行了数值实现，并用它考察了这些系统的全局遍历程度。文中建议将前人关于量子混沌的大量研究结果推广到这些光线分裂问题。特别地，我们指出了Gutzveler迹公式的一个推广，以涵盖射线分裂。
We consider wave systems in which rays split on reflection from sharp boundaries. Examples include the Schroedinger equation with the potential changing discontinuously across a surface, electromagnetic waves in a region with a discontinuous dielectric constant, elastic media with a clamped or free boundary, etc. By introducing a Monte Carlo treatment of the rays, it is possible to define chaotic rays via the standard Lyapunov number criterion. Numerical implementation of the Monte Carlo ray technique is carried out for the example of elastic media, and is utilized to investigate the extent to which these systems are globally ergodic. It is suggested that results from previous extensive work on quantum chaos without ray splitting can be extended to these ray splitting problems. In particular, we indicate a generalization of the Gutzwiller trace formula to cover ray splitting.