论文标题
椭圆形台球中的分叉和异常光谱积累
Bifurcation and anomalous spectral accumulation in oval billiard
论文作者
论文摘要
经典动力学系统表明分叉的量子椭圆形台球的光谱统计是根据两点相关函数（TPCF）的数值研究，该函数定义为在特定能量间隔下找到两个水平的概率密度。发现分叉点处的特征力水平显示出异常的积累，这被观察到TPCF的周期性尖峰振荡。我们分析了位于相空间中各种经典轨迹上的本征函数，发现振荡是从相位空间中的有限区域提供的，其中包含分叉轨道。我们还表明，振荡周期与Gutzwiller Trace公式获得的分叉轨道对半经典TPCF的贡献时期非常吻合。
Spectral statistics of quantum oval billiard whose classical dynamical system shows bifurcations is numerically investigated in terms of the two-point correlation function (TPCF) which is defined as the probability density of finding two levels at a specific energy interval. The eigenenergy levels at bifurcation point is found to show anomalous accumulation which is observed as a periodic spike oscillation of the TPCF. We analyzed the eigenfunctions localizing onto the various classical trajectories in the phase space and found that the oscillation is supplied from a limited region in the phase space, which contains the bifurcating orbit. We also show that the period of the oscillation is in good agreement with the period of a contribution from the bifurcating orbit to the semiclassical TPCF obtained by Gutzwiller trace formula.
