Bogoliubov谱的微扰法

Perturbation method of Bogoliubov spectrum

在冷原子物理中研究超流问题时,需要求解准粒子的Bogoliubov激发谱,而这个过程是通过对体系的哈密顿量做Bogoliubov变换得到.对于简单体系,可直接对哈密顿量矩阵对角化,但当体系涉及多个能带时,哈密顿量矩阵形式复杂,计算难度很大.本文提出利用非厄米矩阵微扰的方法对角化哈密顿量,同时由微扰近似波函数构成Bogoliubov变换矩阵完成哈密顿量的Bogoliubov变换.

When studying superfluid problems in cold atomic physics,it is necessary to solve the Bogoliubov excitation spectrum of quasi⁃particles,and this process is obtained by Bogoliubov transformation of the Hamiltonian of the system.For a simple system,the Hamiltonian matrix can be diagonalized directly,but when the system involves multiple energy bands,the Hamiltonian matrix is complex and difficult to calculate.In this paper,the Hamiltonian is diagonalized by the perturbation method of non⁃Hermitian matrix,and the Bogoliubov transformation matrix is formed by the perturbation approximate wave function to complete the Bogoliubov transformation of the Hamiltonian.