正方体量子台球的半经典分析(英文)

Semiclassical analysis of the cubic billiards

近几年,量子台球问题引起人们的广泛兴趣.以前有很多对二维量子台球做过研究,相对于二维台球来说,三维台球更接近实际体系.本文以三维正方体量子台球为例,利用半经典闭合轨道理论计算了正方体量子台球中的经典开轨道,并研究量子谱函数与经典轨道长度之间的对应关系,发现他们之间对应的很好.这将有助于我们分析开放型量子台球中输运性质问题.利用这种方法物理图像清晰,计算量小并且可以帮助理解一些混沌体系的性质.这是半经典理论为联系量子力学与经典力学起桥梁作用的又一证明。

Quantum billiards has attracted much interest recent years.There are many works on the two-dimensional billiards（2D）.Compare with the 2D billiards,the three-dimensional（3D） billiards approaches with the actual system better.Taking the cubic billiards as an example,using the closed orbit theory（COT）,we find the classical open orbits and study the correspondence between the quantum spectra and the length of classical open orbits in the 3D billiard system.The peaks＇ locations of the quantum spectra match with the length of the classical open orbits very well.This will help us to analyze the transport property through an open billiards.By this method,the physical image is clear,the computation is easier and it can help us to understand the character of some chaotic systems better.This is another example showing that semiclassical method provides a bridge between quantum and classical mechanics.