矩形弹子球中的量子谱和经典周期轨道(英文)

Quantum spectra and classical periodic orbits in a rectangular billiard

利用SU(2)相干态的表示,我们构造了二维矩形弹子球中与经典周期轨道对应的波函数.经典周期轨道和量子波函数之间的关系可以通过物理图像清晰的表示出来.另外,利用周期轨道理论,我们计算了二维矩形弹子球体系的量子谱的傅立叶变换ρ(L).变换谱|ρN(L)|2对L图像中的峰可以和粒子在二维矩形腔中运动的经典轨迹的长度相比较.量子谱中的每一条峰正好对应一条经典周期轨道的长度,表明量子力学和经典力学的对应关系.

By using the representation of SU（2） coherent states, we construct the wave functions related to the classical periodic orbits in the 2D rectangular billiard. The relation between the classical periodic orbits and the quantum wave functions provide a more physical description of a phenomenon than the true eigenstates in mesoscopic systems. Furthermore, by using the periodic orbit theory, we calculate the Fourier transform ρ （L） of the quantum spectra of the two-dimensional rectangular billiard system. The resulting of the peaks in plots of ｜ρN（L）｜2 versus L are compared to the lengths of the classical periodic orbits of the particle moving in the 2D rectangular cavity. The agreement of the peaks between ｜ρN（ L ）｜^2 and the length of the classical periodic orbit suggests the correspondence of quantum mechanics and classical mechanics.