玻色子体系的Bogoliubov变换  

Bogoliubov transformation in Boson system

作　　者：白伊秀 胡洁[1] BAI Yixiu;HU Jie(Department of Physics,Capital Normal University,Beijing 100048)

机构地区：[1]首都师范大学物理系,北京100048

出　　处：《首都师范大学学报（自然科学版）》2021年第1期10-13,30,共5页Journal of Capital Normal University：Natural Science Edition

基　　金：国家自然科学基金青年科学基金项目(21503138)。

摘　　要：对于满足反对易关系的费米子体系,Bogoliubov变换是幺正变换,可以直接对体系哈密顿量进行矩阵对角化,而玻色子体系满足对易关系,不能直接进行矩阵对角化.本文以玻色子体系为研究对象,通过对哈密顿量进行改造,实现对角化,使其在自身表象下表示,并且此方法可以推广至高维自旋系统.The Bogoliubov transformation was a unitary transformation for the fermion system satisfying the an⁃ti⁃commutation relation,which can directly diagonalize the Hamiltonian of the system,while the boson system sat⁃isfied the commutative relation and cannot directly diagonalize the matrix.In this paper,the boson system was tak⁃en as the research object,and the Hamiltonian was transformed to be diagonalized so that it can be represented in its own representation,and this method can be extended to the high⁃dimensional spin system.

关 键 词：冷原子 玻色子 费米子 Bogoliubov变换 幺正变换 

分 类 号：O411[理学—理论物理]