论文标题
在哈密顿动力学系统中检测分叉点检测的量子机械方法
Quantum Mechanical Approach to Bifurcation Point Detection in Hamiltonian Dynamical Systems
论文作者
论文摘要
有界量子系统的能级统计数据（其经典动力学系统表现出分叉），使用两点相关函数（TPCL）研究，该函数在分叉点在分叉点上表现出周期性的尖峰振荡，因为水平的积累称为壳效应。 TPCL的尖峰振荡通过降低的卡方值进行了分析，该值降低了，该值在分叉点时呈现出突然的增加，从而产生了一种新颖的检测方法。使用此方法，我们尝试从数值检测柠檬形台球的分叉点。
Energy level statistics of a bounded quantum system, whose classical dynamical system exhibits bifurcations, is investigated using the two-point correlation function (TPCL), which at the bifurcation points exhibits periodic spike oscillations owing to the accumulation of levels called the shell effect. The spike oscillations of the TPCL is analyzed by the reduced chi-squared value which deduced to exhibit abrupt increases at bifurcation points, thereby yielding a novel detection approach. Using this method, we attempt to numerically detect the bifurcation points of a lemon-shaped billiard.
