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By comparison, two different generators can diagonalize the Hamiltonian and eigenvalue of systems are nearly equal.

比较发现，两种情况都可以对角化系统，计算出的系统本征值略微不同。

Theoretical analysis indicates that the unitary matrix can accurately and simultaneously diagonalize the two matrices.

理论分析表明，该矩阵可以使两个正定矩阵同时精确对角化。

For nonlinear harmonic oscillators, we close the flow equations and acquired an explicit expression of energy-level. For nonlinear-coupled harmonic oscillators, we close the flow equations and diagonalize the Hamiltonian by numerical analysis methods.

对非线性谐振子系统，计算出系统参数随流参数变化的一组方程及系统的能级；对耦合的非线性谐振子系统，得出系统参数随流参数变化的一组非线性方程，数值分析对角化了系统。

We then diagonalize the matrix C and obtain the eigenvalue spectrum and eigenvectors. The large eigenvalues which go beyond the upper bound of the random matrix, i.e., the Wishart matrix, reflect the local correlations between stocks. The largest eigenvalue corresponds to the market mode, and next large eigenvalues represent the interactions between stocks in a same sector.

进一步，通过对角化，我们得到矩阵C的特征值谱和特征向量，超过随机的Wishart矩阵特征值谱上边界的特征值反映了股票间的局域关联，其中最大的特征值对应于市场模式，其余的次大特征值代表了同一板块内股票间的相互作用。

For nonlinear harmonic oscillators systems of coordinate coupling and momentum-coupling, one obtains a group differential equations for physical parameters about flow parameter by the numerical analysis method, one finds this method can diagonalize the Hamiltonian.

通过数值分析物理参数随流参数变化规律，给出了对角化的哈密顿量。

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. The particle number difference of species A between the two wells is studied analytically.

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。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。