相互作用玻色气体的截断近似格林函数  

Truncated Approximate Green’s Functions for Interacting Bose Gases

作　　者：郑菡蕾 ZHENG Han-lei(Shenyang University of Chemical Technology,Shenyang 110142,China)

机构地区：[1]沈阳化工大学理学院,辽宁沈阳110142

出　　处：《沈阳化工大学学报》2021年第2期188-192,共5页Journal of Shenyang University of Chemical Technology

摘　　要：对玻色-爱因斯坦凝聚体凝聚温度和凝聚比例等基本性质的研究,目前已经得到不少重要的理论结果.这些结果往往基于微扰理论,计算非常繁复,而且主要适用于弱相互作用(或者稀薄气体)的情况.采用双时格林函数的运动方程对相关问题进行初步研究,从Bogoliubov近似后的哈密顿量出发,考虑四算符项,讨论两个截断近似方案:第一种是把高阶格林函数中的粒子数算符用其平均值替代;第二种是不仅把粒子数算符简化为常数,而且把一对产生或者湮灭算符(配对算符)也替代为其平均值.粒子数平均值利用正常格林函数通过谱定理来自洽计算;配对算符的平均值基于反常格林函数自洽计算.计算表明:第一种方案的精确程度类似于Bogoliubov近似;第二种方案能够较好反映相互作用势对系统的影响,但在求解粒子数和配对算符平均值时遇到紫外发散问题.发散的起因可能在于把依赖于动量的相互作用势简单地近似为一个与动量无关的常数.The condensation temperature and condensation fraction of Bose-Einstein condensates have been extensive studied.Many important theoretical results have been obtained based on perturbation theory.Usually the calculation is very complicated and the results hold mainly for the weakly interacting systems(or rarefied gas).In this thesis we treat the interacting Bose gases by the two-time Green’s function method.The Hamiltonian is simplified by the Bogoliubov approximation but retaining the four-operator term.In order to get the closed equations of motion,two decoupling schemes are employed to the high-order Green’s function truncation.In the first scheme,the particle number operator which appears in the high-order Green’s functions can be extracted by replacing it with its average value.In the second scheme,both the particle number operator and the pairing operator(two creation or annihilation operator)are extracted from the high-order Green’s functions.The calculations show that the former scheme does not go far beyond the Bogoliubov approximation.The latter can reflect the influence of interactions quite well,but leads to ultraviolet divergence when calculating the average values of the particle number operator and the pairing operator.

关 键 词：相互作用玻色气体 凝聚温度 凝聚比例 格林函数 截断近似 

分 类 号：O469[理学—凝聚态物理]