论文标题
量子三角图的统计和动力学特性
Statistical and dynamical properties of the quantum triangle map
论文作者
论文摘要
我们研究了量子三角图的统计和动力学特性，其经典对应物可以表现出千古来和混合动力学，但绝不是混乱的。数值结果表明，即使潜在的经典动力学并不混乱，近年性是频谱和本征函数遵循随机矩阵理论的预测的充分条件。另一方面，诸如超时订购的相关器（OTOC）等动力学数量和谐波数量在半经典限制中显示出增长率消失，这与经典动力学的lyapunov指数为零。我们的发现表明，虽然光谱统计数据可用于检测登山性，但OTOC和谐波数量是混乱的诊断。
We study the statistical and dynamical properties of the quantum triangle map, whose classical counterpart can exhibit ergodic and mixing dynamics, but is never chaotic. Numerical results show that ergodicity is a sufficient condition for spectrum and eigenfunctions to follow the prediction of Random Matrix Theory, even though the underlying classical dynamics is not chaotic. On the other hand, dynamical quantities such as the out-of-time-ordered correlator (OTOC) and the number of harmonics, exhibit a growth rate vanishing in the semiclassical limit, in agreement with the fact that classical dynamics has zero Lyapunov exponent. Our finding show that, while spectral statistics can be used to detect ergodicity, OTOC and number of harmonics are diagnostics of chaos.
