本文選題：兩分量玻色-愛因斯坦凝聚 + 集體激發(fā)模��； 參考：《新疆師范大學(xué)》2017年碩士論文

【摘要】：近年來,兩分量及多分量的玻色-愛因斯坦凝聚(Bose-Einstein condensation,簡稱BEC)問題的研究已逐漸深入,并成為凝聚態(tài)物理學(xué)研究的熱點。單獨研究一個粒子的性質(zhì)以及每個粒子之間的相互作用規(guī)律并不是那么容易,這就需要引入集體激發(fā)的概念,BEC的集體激發(fā)作為一個基本問題對于多體問題的研究顯然是至關(guān)重要的。描述集體激發(fā)的方法包括:求解博戈留波夫·德熱納(Bogoliubov de gennes,簡稱BDG)方程組的方法、變分方法、標(biāo)度理論的方法、托馬斯費米(Thomas-Fermi,簡稱TF)近似下的流體動力學(xué)方程直接求解的方法等。本文利用標(biāo)度理論,并用完全解析的方法研究兩分量球?qū)ΨQ玻色-愛因斯坦凝聚(two-component Bose-Einstein condensation,2BEC)的集體激發(fā)模。迄今為止,國內(nèi)外都沒有用標(biāo)度理論研究2BEC的工作。對于多分量BEC這樣的復(fù)雜問題,一般采用解析和數(shù)值模擬相結(jié)合的方法,而本文采用簡明但難度較大的完全解析方法。先根據(jù)描述2BEC的動力學(xué)特征的耦合格羅斯·皮塔耶夫斯基(coupled Gross-Pitaevskii,簡稱CGP)方程引出在TF近似下的流體動力學(xué)方程,推導(dǎo)標(biāo)度理論下的TF近似流體動力學(xué)方程,推導(dǎo)求解軸對稱2BEC低能激發(fā)模的方程組。然后,求出球隊稱2BEC高階和低階單極子模頻率和振幅的解析表達(dá)式,包括描述兩分量相互作用的耦合項系數(shù)等相關(guān)量的解析表達(dá)式。最后,對解析表達(dá)式進(jìn)行無量綱化,通過計算研究高階和低階單極子模頻率及兩分量混合程度隨耦合相互作用強度的關(guān)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.
【學(xué)位授予單位】：新疆師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O469

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 李冠強;彭娉;;耦合Gross-Pitaevskii方程的變分原理[J];西北師范大學(xué)學(xué)報(自然科學(xué)版);2009年05期

，

本文編號：1928157