International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China.
Center for Theoretical Physics, Department of Physics, Capital Normal University, Beijing 100048, China.
Phys Rev E. 2019 Nov;100(5-1):052206. doi: 10.1103/PhysRevE.100.052206.
The effect of the Kolmogorov-Arnold-Moser (KAM) theorem in quantum systems is manifested in dividing eigenstates into regular and irregular states. We propose an effective method based on the Wannier basis in phase space to illustrate this division of eigenstates. The quantum kicked-rotor model is used to illustrate this method, which allows us to define the area and effective dimension of each eigenstate to distinguish quantitatively regular and irregular eigenstates. This Wannier basis method also allows us to define the length of a Planck cell in the spectrum that measures how many Planck cells the system will traverse if it starts at the given Planck cell. Moreover, with this Wannier approach, we are able to clarify the distinction between the KAM effect and Anderson localization.
量子系统中的柯尔莫哥洛夫-阿诺尔德-莫泽（KAM）定理的作用表现为将本征态划分为规则态和不规则态。我们提出了一种基于相空间中的瓦尼尔基的有效方法来说明这种本征态的划分。量子受迫转子模型被用来阐述这种方法，这使我们能够定义每个本征态的面积和有效维数，以定量地区分规则和不规则本征态。这种瓦尼尔基方法还使我们能够定义谱中的普朗克细胞长度，它衡量了系统从给定的普朗克细胞开始时将穿越多少个普朗克细胞。此外，通过这种瓦尼尔方法，我们能够澄清 KAM 效应和安德森局域化之间的区别。
