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。
It is just the difficulty that the strongly correlated electron systems can not be studied by analytical methods , a variety of simulative numerical methods come out sequentially . there are a few typical methods such as the exact diagonalization ( ed ) , the qutum monte carlo ( qmc ) , the variation monte carlo ( qmc ) , the renormalization group ( rg ) , and the density matrix renormalization group ( dmrg ) and so on 正是强关联系统遇到了解析研究的困难，各种数值模拟方法才相继出现，最典型的数值方法有：严格对角化( ed ) ，量子蒙特卡洛( qmc )模拟、变分蒙特卡洛模拟( vmc ) 、数值重整化群( rg )以及密度矩阵重整化群( dmrg )等。
In this paper , these two methods are employed to consider three kinds of singular perturbation boundary value problems . in the first section , the existence of solution for a class of non - linear systems with three - point boundary problem is obtained by applying the differential inequality theory . in the second section , we use the differential inequality theory to discuss the non - monotone interior layer solution for one kind of singularly perturbed quasilinear boundary value problems with a turning point . in the third section , the diagonalization method is applied to study the existence of solution for a class of vector differential systems with two - point or three - point boundary problems . meanwhile , the asymptotic estimate of the solution as well as its first - order derivative and its second - order derivative is obtained 在第一部分中，我们应用微分不等式理论证明了一类非线性系统三点边值问题解的存在性；在第二部分中，运用微分不等式理论研究了一类带有转向点的拟线性奇摄动边值问题的非单调内层解；在第三部分中，利用对角化方法研究了一类向量二点或者三点边值问题解的存在性，并获得解及它的一、二阶导数的渐近估计。
Expanding the system ' s hamiltonian to a real symmetric matrix in an appropriate orthogonal basis vector and then diagonalizing it , we get the energy spectrum of the system and calculate the energy level spacing distribution function and the spectral rigidity . then we study the statistical character of the energy spectrum under the changing of magnetic field intension and find that the system ' s motion transfers from regular to chaos gradually 将系统的哈密顿量在一个适当的正交基矢下展开并对角化，得到系统的能谱，分别计算系统能谱的能级间距分布函数和谱刚度，研究了该系统量子能谱的统计特征随磁感应强度大小的改变而表现出的系统运动由规则到混沌的渐进变化。
By using the asymptotic analysis method and the diagonalization technique , considers the singular perturbation of boundary value problem for system of third order nonlinear integro - differential equation . under appropriate assumptions , the existence of the solution of perturbation problem has been proved and a asymptotic expansion of the solution and the estimation of the corresponding remainder term are geven as well 研究三阶非线性积分微分方程组边值问题的奇摄动.在适当的条件下，利用渐近分析方法和对角化技巧，证得解的存在性并给出解的渐近展开式及其余项估计
By using the new method , the eigenstate of xxz antiferromagnetic model is solved , which is revealed to be 5 ? l , l ) coherent state . in the third chapter , we discussed the relation between the bogoliubov - valatin transformation and the algebraic method based upon the bcs model hamiltonian at first . then , we diagonalized the ssh model hamiltonian for the first time by using the algebraic diagonalization method 第三章我们首先使用bogoliubov - valatin变换对角化和新的代数对角化两种方法，将bcs模型的哈密顿量对角化，并对两种对角化方法作了比较、讨论；其后，本文首次给出了代数对角化方法在ssh模型中的应用，并且其结果也与bv变换法的作了同上面bcs模型类似的讨论。
Since the instinct unsupervised learning of the rbf network and blind signal processing are in essence unsupervised learning procedures , therefore the algorithm based on rbf seems rational . 2 ) according to signals high order cumulant . bss problems are transformed into diagnolization of special matrix 2 )在研究随机过程理论的基础上，从信号的高阶累积量出发，将线性西安理工大学硕士学位论文混合盲分离问题转化为矩阵的对角化问题，大大简化了bss算法的复杂度。
Nevertheless , the results provided by these methods are all inaccurate . in this thesis , in order to overcome the drawbacks , we reconstruct the bose - hubbard model hamiltonian with differential realization of bosonic operators , and investigate the exact numerical solutions of the one dimension bose - hubbard model . firstly , energy matrices can be generated rapidly by using a mathematica package 首先利用mathematica程序快速生成模型在各种位型下能量矩阵，然后将该程序的结果直接作为其它矩阵对角化程序的输入而求出该模型在相应位型下的本征值和相应的本征波函数。
