用标度理论研究球对称两分量的玻色—爱因斯坦凝聚的低能集体激发模

发布时间：2018-05-24 07:08

本文选题：两分量玻色-爱因斯坦凝聚 + 集体激发模　；参考：《新疆师范大学》2017年硕士论文

【摘要】：近年来,两分量及多分量的玻色-爱因斯坦凝聚(Bose-Einstein condensation,简称BEC)问题的研究已逐渐深入,并成为凝聚态物理学研究的热点。单独研究一个粒子的性质以及每个粒子之间的相互作用规律并不是那么容易,这就需要引入集体激发的概念,BEC的集体激发作为一个基本问题对于多体问题的研究显然是至关重要的。描述集体激发的方法包括:求解博戈留波夫·德热纳(Bogoliubov de gennes,简称BDG)方程组的方法、变分方法、标度理论的方法、托马斯费米(Thomas-Fermi,简称TF)近似下的流体动力学方程直接求解的方法等。本文利用标度理论,并用完全解析的方法研究两分量球对称玻色-爱因斯坦凝聚(two-component Bose-Einstein condensation,2BEC)的集体激发模。迄今为止,国内外都没有用标度理论研究2BEC的工作。对于多分量BEC这样的复杂问题,一般采用解析和数值模拟相结合的方法,而本文采用简明但难度较大的完全解析方法。先根据描述2BEC的动力学特征的耦合格罗斯·皮塔耶夫斯基(coupled Gross-Pitaevskii,简称CGP)方程引出在TF近似下的流体动力学方程,推导标度理论下的TF近似流体动力学方程,推导求解轴对称2BEC低能激发模的方程组。然后,求出球队称2BEC高阶和低阶单极子模频率和振幅的解析表达式,包括描述两分量相互作用的耦合项系数等相关量的解析表达式。最后,对解析表达式进行无量纲化,通过计算研究高阶和低阶单极子模频率及两分量混合程度随耦合相互作用强度的关系。
[Abstract]:In recent years, the study of Bose-Einstein condensation (BECs) of two-component and multi-component Bose-Einstein condensation (BECs) has become a hot topic in condensed matter physics. It is not easy to study the properties of a particle alone and the law of interaction between each particle. Therefore, it is necessary to introduce the concept of collective excitation. As a basic problem, the collective excitation of bec is obviously very important to the study of multi-body problems. The methods used to describe collective excitation include the method for solving the Bogoliubov de Gennesn equations of Bogoliubov de Gennesn, the variational method, and the method for scaling theory. Thomas Fermi Thomas-Fermie (TF) approximation for the direct solution of hydrodynamic equations and so on. In this paper, the collective excitation modes of two-component spherical symmetric Bose-Einstein condensate two-component Bose-Einstein condensation2BECs are studied by using scale theory and complete analytic method. Up to now, scale theory has not been used to study 2BEC at home and abroad. For complex problems such as multi-component BEC, the analytical method and numerical simulation method are generally used, while the complete analytical method which is simple but difficult is used in this paper. Based on the coupled Gross-Pitaevskii equation, which describes the dynamic characteristics of 2BEC, the hydrodynamic equation under TF approximation is derived, and the TF approximate hydrodynamic equation based on scaling theory is derived. The equations for solving axisymmetric 2BEC low-energy excitation modes are derived. Then, the analytical expressions of frequency and amplitude of unipolar modes of high order and low order for 2BEC are obtained, including the analytical expressions describing the coupling term coefficients of the interaction of two components. Finally, the analytical expression is dimensionless, and the relationship between the frequency of high order and low order monopole modes and the degree of mixing of two components with the coupling interaction intensity is studied.
【学位授予单位】：新疆师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O469

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