Floquet变换及其在电子结构计算中的应用  

FLOQUET TRANSFORMATION AND ITS APPLICATION IN THE CALCULATION OF ELECTRONIC STRUCTURES

作　　者：张丹[1] 付佳[1] 田虹 Zhang Dan;Fu Jia;Tian Hong(Patent Examination Cooperation(Beijing)Center of the Patent Office,CNIPA,Beijing 100160,China)

机构地区：[1]国家知识产权局专利局专利审查协作北京中心,北京100160

出　　处：《计算数学》2024年第3期385-396,共12页Mathematica Numerica Sinica

摘　　要：Floquet变换是研究具有周期平移不变性算子的数学工具,本文从这个视角讨论了周期体系量子特征值问题的基本数学性质,由Floquet变换得到Bloch函数,通过Floquet逆变换定义Wannier函数.在此过程中,证明了作用于周期单元平方可积函数的算子H(k)的自伴性及预解集紧性、Wannier函数作为L^(2)(R^(d))基底的正交性与完备性.还证明了孤立能带关于的连续可微性,介绍了非孤立能带组的光滑化.最后,从Wannier函数的Floquet变换出发,介绍了能带的插值计算.Floquet transform is a mathematical tool for studying operators with periodic translation invariance.This paper discusses the basic mathematical properties of quantum eigenvalue problems of periodic systems from this perspective.The Bloch function is obtained by the Floquet transformation,and the Wannier function is defined by the inverse of Floquet transformation.In this process,the operator H(k)is proved for square-integrable functions of periodic units.The self-adjoint and resolvable set compactness,Wannier function as L^(2)(R^(d))Orthogonality and completeness of the basis.The continuous differentiability of the isolated energy band with respect to k is also proved.The smoothing of non-isolated band groups is introduced.Finally,based on the Floquet transform of Wannier function,the interpolation calculation of energy band is introduced.

关 键 词：Floquet变换 Wannier函数 量子特征值 第一性原理 能带插值计算 

分 类 号：O24[理学—计算数学]