量子三角映射的统计和动力学性质
Statistical and dynamical properties of the quantum triangle map
摘要：
我们研究了量子三角映射的统计和动力学性质，它的经典对应物可以表现出遍历和混合动力学，但从来没有混沌。数值结果表明，遍历性是一个充分条件的频谱和本征函数遵循随机矩阵理论的预测，即使潜在的经典动力学是不是混沌。另一方面，动力学量，如外的时间有序相关（OTOC）和谐波的数量，表现出增长率消失的半经典极限，在协议的事实，经典动力学的李雅普诺夫指数为零。我们的研究结果表明，虽然频谱统计可以用来检测遍历性，OTOC和谐波的数量是混沌的诊断。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
