Department of Electrophysics, National Chiao Tung University, 1001 Ta-Hsueh Rd., Hsinchu 30010, Taiwan.
Institute of Optoelectronic Science, National Taiwan Ocean University, 2 Pei-Ning Rd., Keelung 20224, Taiwan.
Phys Rev E. 2017 Jan;95(1-1):012217. doi: 10.1103/PhysRevE.95.012217. Epub 2017 Jan 30.
A general method is developed to characterize the family of classical periodic orbits from the quantum Green's function for the two-dimensional (2D) integrable systems. A decomposing formula related to the beta function is derived to link the quantum Green's function with the individual classical periodic orbits. The practicality of the developed formula is demonstrated by numerically analyzing the 2D commensurate harmonic oscillators and integrable quantum billiards. Numerical analyses reveal that the emergence of the classical features in quantum Green's functions principally comes from the superposition of the degenerate states for 2D harmonic oscillators. On the other hand, the damping factor in quantum Green's functions plays a critical role to display the classical features in mesoscopic regime for integrable quantum billiards, where the physical function of the damping factor is to lead to the coherent superposition of the nearly degenerate eigenstates.
发展了一种通用方法，用于从二维（2D）可积系统的量子格林函数中描述经典周期轨道族。推导出一个与β函数有关的分解公式，将量子格林函数与单个经典周期轨道联系起来。通过数值分析 2D 简谐振荡器和可积量子 billiards，验证了所发展公式的实用性。数值分析表明，量子格林函数中经典特征的出现主要来自于 2D 谐振子简并态的叠加。另一方面，量子格林函数中的阻尼因子在可积量子 billiards 的介观区域中显示经典特征起着关键作用，其中阻尼因子的物理作用是导致近简并本征态的相干叠加。
