量子本征值问题的自洽近似法

利用算符弱等价的办法提出量子力学中求解本征值问题的一种新的近似方法－－自洽近似法，它兼有微扰论和变分法的特征。几个例子演示了该方法的有效性。     

de Sitter时空背景下的熵

从ｄｅＳｉｔｔｅｒ时空背景下的Ｋｌｅｉｎ－Ｇｏｒｄｏｎ方程出发，利用Ｂｒｉｃｋ－ｗａｌｌ方法计算了宇宙的自由能和熵。结果表明，宇宙的熵与Ｓｃｈｗａｒｚｓｃｈｉｌｄ黑洞一样，也为视界面积的１／４。可见，ｂｒｉｃｋ－ｗａｌｌ方法具有更广泛的适用于，不但可以计算黑洞的熵，而且可以计算宇宙的熵。     

Macroscopic Quantum Phenomena and Topological Phase Interference Effects in Single-Domain Magnets

The tunneling of macroscopic object is one of the most fascinating phenomena in condensed matter physics. During the last decade, the problem of quantum tunneling of magnetization in nanometer-scale magnets has attracted a great deal of theoretical and experimental interest. A review of recent theoretical research of the macroscopic quantum phenomena in nanometer-scale single-domain magnets is presented in this paper. It includes macroscopic quantum tunneling (MQT) and coherence (MQC) in single-domain magnetic particles, the topological phase interference or spin-parity effects, and tunneling of magnetization in an arbitrarily directed magnetic field. The general formulas are shown to evaluate the tunneling rate and the tunneling level splitting for single-domain AFM particles. A nontrivial generalization of Kramers degeneracy for double-well system is provided to coherently spin tunneling for spin systems with m-fold rotational symmetry. The effects induced by the external magnetic field have been studied, where the field is along the easy, medium, hard axis, or arbitrary direction.     

三原子直线分子的测量

对于三个原子组成的直线分子哈密顿系统，对角化后等效为两个相互独立的量子谐振子和一个自由粒子，应用热场动力学理论，得到了有限温度下测量坐标和动量的量子涨落。     

Quantum Size Effect of the Magnetism of an Electron in a Metal Layer of the Layered Compounds M/I/M/I…

The energies and the magnetization of an electron in a piece of metal in the structure of Metal/Insulator/Metal/Insulator…(M/I/M/I…), in a magnetic field, at high temperature, and in range of quantum size thickness of the piece of metal layer have been obtained. The results show that when the thickness of the metal layer becomes smaller, the orbital magnetism of the charged particles which collide with the wall of the metal layer is to vary from diamagnetism to paramagnetism. The smaller the thickness of the metal layer becomes, the more particles will collide with the boundary of the metal layer, and then the paramagnetism becomes stronger. Finally, when the thickness of the metal layer becomes very small (＜100 nm), all of the orbital diamagnetism will reverse to paramagnetism, and then the paramagnetization will be almost a maximum constant.     

温度对冷槽离子质心声子的影响

针对单声子在门操作中的特殊作用,采用松原函数的方法讨论了冷槽离子模型中温度对质心声子数的影响.结果表明,控制离子内态保持在基态的温度量级是mK,这与采用格林函数方法的计算结果一致,而单声子的控制温度在μK量级.所以在门运算过程中,主要考虑质心声子态的影响.     

n维简谐势阱中粒子的态密度

应用半经典近似法计算任意维数非相对论性理想体系处于简谐外势中的量子态密度，得出解析的表达式，并进行讨论．揭示了简谐外势对系统性质的影响．特别是对于二维系统，使之从准长程序转变为长程序，对于一维系统，使之从无序转变为准长程序     

在整体色对称模型下的夸克囚禁势

在整体色对称模型框架下，基于已经确定好的双定域场，推导了等效的夸克夸克相互作用势．结果表明除了通常的单π及单σ交换项外，自动出现了带有屏蔽因子的囚禁势．     

q形变量子群Rq（sl（2））的有限维单模

主要讨论单李代数U（sl（2））的一类新的q形变量子群Rq（sl（2））,Uq（sl（2））可以看作Rq（sl（2））的一个子代数.在复数域k上且q是本原的d次单位根的条件下给出Rq（sl（2））的有限维单表示的分类.     

Lindblad型开放量子系统最优控制

对于伴随着松弛和耗散的Lindblad型开放量子系统,采用基于Liouville超算符变换的方法,将开放量子系统的动力学微分方程的矩阵表达形式转化成向量表达以简化微分方程的求解。以系统被控状态到达目标状态的期望值为性能指标,对变换后的开放量子系统进行最优控制律的设计,以达到状态转移的目的。在MATLAB环境下以2能级开放量子系统为例进行了系统仿真实验。对控制参数的变化对系统的布居数转移概率及其控制时间的影响进行了对比实验,并对实验结果进行了对比分析。

Abstract：

In order to solve the state of an open quantum system with relaxation and dissipation,the dynamical equation of the system in matrix was transformed into vector form in Liouville space. Taking the expectation value for the state under control reaching the target state as performance indicators,an optimal control function was derived for the system transformed. The control a 2-level open quantum system was simulated on in MATLAB. The influence to population transfer probability and control time caused by changing of parameters were analysed contrastively.