Bose - einstein condensate ? a gas so cold that the atoms have lost their individual identity ? can act on sound like an expanding universe does on light , either by literally flying apart or by being manipulated using a magnetic field to give the same effect 一团玻色?爱因斯坦凝聚（一种冷到原子会丧失其个体性的气体） ，可以像膨胀的宇宙对光的作用一样，来对声音作用，不管是令其飞散，或是用磁场来操纵，都可以得到同样的效应。
A bose - einstein condensate ? a gas so cold that the atoms have lost their individual identity ? can act on sound like an expanding universe does on light , either by literally flying apart or by being manipulated using a magnetic field to give the same effect 一团玻色?爱因斯坦凝聚（一种冷到原子会丧失其个体性的气体） ，可以像膨胀的宇宙对光的作用一样，来对声音作用，不管是令其飞散，或是用磁场来操纵，都可以得到同样的效应。
On the other hand , various techniques using the dhbs have been applied in optical traps for microscopic particles , guiding , cooling and trapping for neutral atoms as well as in manipulations and control of coherent matter waves ( i . e . , bose - einstein condensations ( bec ) ) and so on 同时，其他的一些研究小组开展了暗中空光束在光阱与微粒的操纵、中性原子的激光导引、冷却与囚禁以及相干物质波(如玻色-爱因斯坦凝聚， bec )的操纵与控制等领域的应用研究。
2 . the exact n - soliton solutions of the nonlinear schrodinger equation with time - dependent linear potential are presented by employing the darboux transformation method . as the special cases , bright soliton - solutions are obtained in bose - einstein condensates , and their properties and interaction between solitons are discussed as well 利用darboux变换，对含时线性势的非线性薛定谔方程进行求解，并研究在耦合外场作用下，准一维玻色-爱因斯坦凝聚体中亮孤子的动力学行为。
A boson josephson junction ( bjj ) formed in a weakly coupled double - bec has been discussed intensively . based on mean - field theory ( mft ) , which gives rise to the gross - pitaevskii equation , interesting phenomena such as macroscopic quantum self - trapping ( mqst ) , and n - phase state , where the time - averaged quantum phase difference across the junction equals n have been predicted 目前由弱耦合双组分bec所构成的玻色约瑟夫森结( bjj )成为研究热点，在平均场理论基础上预言了许多有趣的现象如宏观量子自捕获( mqst ) ，和-位相态(结间量子位相差的时间平均值为) 。
First , we concisely recall the formation and development of bose - einstein condensa - tion ' s theory and it ' s experimentation . secondly , we briefly intro - duce some properties of weakly interactive bose gases , and derive the nonlinear gross - pitaevskii equation that is the condensate macroscopic wave function ' s equation . thirdly , we give a exam - pie , an approximation analytical solution of the gross - pitaevskii equation in a spherical symmetric harmonic trap is derived by a perturbation theory approach , this solution is consistent with that numerically obtained 全文共分为四章：第一章首先简要的介绍和回顾了玻色-爱因斯坦凝聚理论的产生和发展，以及其实验研究的过程，然后着重介绍了弱相互作用的玻色气体的一些性质，并推导出了凝聚体宏观波函数满足非线性的gp方程，还以球对称的谐振子势为例，用标准的微扰方法求出了定态的gp方程近似解，发现其与已知的数值结果符合得很好。
The further research in the nonlin - ear issue of bose - einstein condensation such as solitons , plays a important role in understanding the main physical features of the condensation , improving theoretical study and the technique . this thesis consists of four chapters . the chapter one in - cludes mainly following three part contents 对玻色-爱因斯坦凝聚体中孤子问题等非线性问题进行深入的研究，对我们了解玻色-爱因斯坦凝聚体的物理特性，以及推进其理论研究和应用技术的发展，都是非常有意义的。
We examin e the generation of bell state in bose - einstein condensates of two interacting species trapped in a double - well configuration analytically and the density of probability for finding the entangled bell state is given . we find that the oscillation amplitude of the probability of density for finding the entangled bell state becomes greater as the ratio of the interspecies interaction strength and the tunneling rate increases , moreover the self - interaction strength of the component a ( b ) has no effect on it . also we use the time - dependent su ( 2 ) gauge transformation to diagonalize the hamilton operator , obtain the berry phase and analytically the time - evolution operator 此外我们还研究了在双阱玻色-爱因斯坦凝聚中纠缠态的演化，研究发现随着组分间相互作用和随穿率的比值的增加系统演化到bell态的概率变大，而且组分自身内在的相互作用对形成bell态的几率没有影响；并且用含时su ( 2 )规范变换对角化哈密顿量得到了系统的berry位相和时间演化算符，并研究了量子随穿过程。
Chapter i is the preface of this thesis . in this part we just tell the history of the bose - einstein condensation , covering the birth of this theory , the exploration in experiments proving the foresee of this theory , progress made in the understanding of the phenomenon , theoretical models for solving it , improvements in the technology and as a result the final implementation in the laboratory . . 第一章主要叙述了对玻色-爱因斯坦凝聚研究的发展历程，包括玻色和爱因斯坦最初对这一理论的阐述、实验上对这一物理现象的探索、理论认识的深化和理论模型方法的提出、实验技术的发展、改进及实验上最终成功的实现。
Witten ' s open string field theory formulate the interaction of bosonic open strings in the language of noncommutative geometry . compactification of matrix theory on the noncommutative torus was argued to correspond to supergravity with constant background three form tensor field . more generally , it has been realised that noncommutative gauge theory arises in the worldvolume theory on d - brane in the presence of a constant background b field in string theory Witten的开弦场论用非对易几何描述了玻色开弦的相互作用；在非对易torus上的矩阵理论的紧化对应于带有常数三形式张量场的超引力；更为普遍的，非对易规范理论可以自然地产生在带有常数b背景场的三维d - brane上。
