Aubry-André模型的Wigner函数和Wigner熵  

Wigner distribution and Wigner entropy of Aubry-Andrémodel

作　　者：从泰和 冯曦曦 高先龙[1] CONG Taihe;FENG Xixi;GAO Xianlong(College of Physics and Electronic Information Engineering,Zhejiang Normal University,Jinhua 321004,China)

机构地区：[1]浙江师范大学物理与电子信息工程学院,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2024年第4期413-417,共5页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(12174346)。

摘　　要：Wigner函数是一种用于可视化量子态在相空间中分布特点的工具.为了探究一维Aubry-André(AA)模型中不同相在相空间中的分布特征,以及拓展—局域转变的临界性中的Wigner熵,对Wigner函数进行了计算.结果显示:当系统处于拓展相时,波函数在坐标空间中展宽,在动量空间中局域化,符合海森堡不确定性原理;相反,当系统处于局域相时,分布特征与之相反.同时,还成功利用Wigner熵标识了拓展—局域转变的相变点,并发现Wigner熵在临界点处达到最大值,与拓展相和局域相中Wigner熵值的降低相比较,有显著差异.该结果为理解AA模型拓展—局域相变提供了新视角.Wigner function provided a great visualization tool for distinguishing different types of quantum states in phase space.In order to study the distribution of different phases of the one-dimensional Aubry-Andrémodel and the Wigner entropy of the critical phase between the extended and localized phases,the Wigner function was calculated and analyzed.It was indicated that when the system was in an extended phase,the eigenmodes were extended in real space but localized in momentum space,and satisfied the Heisenberg uncer-tainty principle.The localized phase was characterized,in contrast,by having exponentially localized eigen-modes in real space.Furthermore,the Wigner entropy was utilized to identify the phase transition point of the localization transition.It was also demonstrated that at the critical point,the Wigner entropy displayed a diver-gent distribution,which was significantly distinct compared with the decrease of Wigner entropy in the extend-ed and localized phases.The presented results could provide a new perspective for understanding the phase transition of AA model.

关 键 词：相空间 WIGNER函数 Aubry-André模型 Wigner熵 

分 类 号：O469[理学—凝聚态物理]