U（5）\leftrightarrow SO（6）过渡区能级间距的极大似然估计方法
Level spacing of U(5) \leftrightarrow SO(6) transitional region with maximum likelihood estimation method
摘要：
本文在IBM框架下，利用无穷维代数方法，系统地研究了U（5）\leftrightarrow SO（6）极限下的量子相变.用极大似然估计（MLE）方法研究了能级统计，以表征过渡区。这些系统的本征值是通过求解Bethe-Anglesian方程，对实验数据进行最小二乘拟合，得到哈密顿常数。我们的结果验证了最近邻间距分布（NNSD）参数对控制参数（c_{s}）的依赖性，并与两个极限值比较，显示了过渡区的混沌行为.为了比较我们的结果与GUE和GOE合奏的两个限制，我们提出了一个新的NNSD分布，并获得了更好的KLD距离的新分布相比，在这两个限制。在\to \infty情形下，总玻色子数依赖性也表现出普适性，即对于每个控制参数值，NNSD都趋于Poisson极限。
英文摘要：
In this paper,a systematic study of quantum phase transition within U(5) \leftrightarrow SO(6) limits is presented in terms of infinite dimensional Algebraic technique in the IBM framework. Energy level statistics are investigated with Maximum Likelihood Estimation (MLE) method in order to characterize transitional region. Eigenvalues of these systems are obtained by solving Bethe-Ansatz equations with least square fitting processes to experimental data to obtain constants of Hamiltonian. Our obtained results verify the dependence of Nearest Neighbor Spacing Distribution's (NNSD) parameter to control parameter (c_{s}) and also display chaotic behavior of transitional regions in comparing with both limits. In order to compare our results for two limits with both GUE and GOE ensembles, we have suggested a new NNSD distribution and have obtained better KLD distances for the new distribution in compared with others in both limits. Also in the case of N\to\infty, the total boson number dependence displays the universality behavior, namely NNSD tends to Poisson limit for every values of control parameter.
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