基于广义Fourier变换的量子输运Green函数方法  

Quantum Transport Green Function Method Based on Generalized Fourier Transform

作　　者：胡跃光 卢朓 姜海燕 HU Yue-guang;LU Tiao;JIANG Hai-yan(School of Mathematical Sciences,Beijing Institute of Technology,Beijing 100081,China;School of Mathematical Sciences,Peking University,Beijing 100875,China)

机构地区：[1]北京理工大学数学与统计学院,北京100081 [2]北京大学数学科学学院,北京100875

出　　处：《数学的实践与认识》2021年第13期194-201,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11671038)。

摘　　要：基于广义Fourier变换理论,给出了量子输运Green函数方法的清晰数学理论解释.利用对含时问题传播子的分析解释了稳态后向Green函数和前向Green函数的数学含义及其物理意义,并严格推导了稳态问题自能项的解析表达式.进一步通过广义Fourier变换,给出了含时问题边界条件的准确表达式,从而搭建了通过引入自能项把稳态及含时量子系统无界区域问题转化到有界区域问题的一般框架.Based on the generalized Fourier transformation,a clear explanation for the Green function method in quantum transport is given.We explain clearly the mathematical theory and physical meaning of the advanced Green function and retarded Green function at equilibrium state,and the definition of self-energy by Green function is rigorously derived.The exact boundary condition for the time-dependent Schrodinger equation is designed by the generalized Fourier transform and present the framework of converting the open boundary quantum system into the finite boundary problem by introducing the self-energy.

关 键 词：广义FOURIER变换 Schr?dinger方程 GREEN函数 自能项 

分 类 号：O413[理学—理论物理]