Institute for Quantum Computing, University of Waterloo, Canada N2L 3G1.
Department of Physics and Astronomy, University of Waterloo, Canada N2L 3G1.
Phys Rev E. 2018 May;97(5-1):052209. doi: 10.1103/PhysRevE.97.052209.
Quantum-classical correspondence in chaotic systems is a long-standing problem. We describe a method to quantify Bohr's correspondence principle and calculate the size of quantum numbers for which we can expect to observe quantum-classical correspondence near periodic orbits of Floquet systems. Our method shows how the stability of classical periodic orbits affects quantum dynamics. We demonstrate our method by analyzing quantum-classical correspondence in the quantum kicked top (QKT), which exhibits both regular and chaotic behavior. We use our correspondence conditions to identify signatures of classical bifurcations even in a deep quantum regime. Our method can be used to explain the breakdown of quantum-classical correspondence in chaotic systems.
混沌系统中的量子经典对应是一个长期存在的问题。我们描述了一种量化玻尔对应原理的方法，并计算了可以期望在 Floquet 系统的周期轨道附近观察到量子经典对应现象的量子数的大小。我们的方法展示了经典周期轨道的稳定性如何影响量子动力学。我们通过分析量子受迫陀螺（QKT）中的量子经典对应来演示我们的方法，该系统表现出规则和混沌行为。我们使用我们的对应条件来识别甚至在深量子区域中经典分岔的特征。我们的方法可用于解释混沌系统中量子经典对应现象的破裂。
