周期轨道附近的量子经典对应
Quantum-classical correspondence in the vicinity of periodic orbits
摘要：
混沌系统中的量子-经典对应是一个长期存在的问题。我们描述了一种方法来量化玻尔的对应原理和计算的量子数的大小，我们可以期望观察到的量子经典对应Floquet系统的周期轨道附近。我们的方法显示了经典周期轨道的稳定性如何影响量子动力学。我们通过分析量子踢顶（QKT）中的量子经典对应来演示我们的方法，该对应具有规则和混沌行为。我们使用我们的对应条件，以确定签名的经典分叉，即使在深量子制度。我们的方法可以用来解释混沌系统中量子-经典对应的破裂。
英文摘要：
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.
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