Wn(n=3—27)原子团簇结构的第一性原理计算

使用密度泛函理论下的第一性原理方法，对W_n原子团簇(n=3—27)的结构特性进行了理论计算. 得到了W_n团簇(n=3—7)的最低能量结构和(n=8—27)的局域能量极小的典型结构. 使用凝胶模型，提出的电子组态1s²1p⁶1d¹⁰2s²1f¹⁴2p⁶3s     

三明治结构Tan(B3N3H6)n+1 团簇的磁性和量子输运性质

利用密度泛函理论和非平衡格林函数方法, 本文对小尺寸团簇Ta_n(B₃N₃H₆)_n+1 (n ≤ 4)的磁性和量子输运性质进行了系统的研究. 计算结果表明, 此类体系采用三明治结构作为其基态并且具有较高的稳定性. 体系的磁矩随团簇尺寸的增大而线性增大. 当把Ta_n(B₃N₃H₆)_n+1团簇耦合到Au电极上时, 形成的Au-Ta_n(B₃N₃H₆)_n+1-Au体系在有限偏压下展示出了较强的自旋过滤能力, 因而可以被看做是一类新型的低维自旋过滤器.     

单粒子薛定谔液体和形变核的转动惯量

将单粒子薛定谔液体理论应用于轴对称形变核的集体运动.也给出了一个相反的例子,即在各向异性谐振子势中处于稳定形变的任意数目的独立核子.而且,通过填充与主量子数n_x,n_y和n_z的可能值相应的单粒子态来构成s-d壳偶偶核:²⁰Ne,²⁴Mg,²⁸Si,³²S和³⁶Ar的基态,并计算了作为谐振子参数hω_x,hω_y和hω_z的函数的这些核的推转模型、刚体模型和稳态模型转动惯量.这些谐振子参数用与质量数A、中子数N、质子数Z和形变参数β有关的非形变参数hω00来描述.这些核的推转模型转动惯量的理论计算结果与实验数据符合甚好.而且,所考虑的轴对称形变核可能是扁椭球形的,也可能不是扁椭球形的,其中²⁴Mg是惟一高度形变的.²⁰Ne和²⁴Mg这两个核的刚体模型和稳态模型转动惯量也与实验数据符合甚好.     

gb→tH－的超对称QCD单圈修正和非退耦效应

在最小超对称标准模型的框架内计算了gb→tH^－过程产生截面的单圈超对称QCD修正.结果发现:若胶子质量和超对称软破缺参数μ或A_t,A_b同量级且趋于很大,就会出现超对称QCD的非退耦效应.大的tanβ值可以提高非退耦的贡献,因此大tanβ情况下,较大的修正结果可能在Tevatron和LHC上观测到.非退耦行为的根本原因在于圈图中的某些耦合顶角正比于超对称质量参数.     

HC2nO+ (n=3-6) 正离子的红外光解离光谱以及理论计算研究

本文利用脉冲激光溅射-超声分子束载带离子源在气相中产生了HC_2nO⁺ (n=3-6)正离子. 通过对贴附CO的络合物离子的红外光解离光谱实验获得了HC_2nO⁺正离子在1600∽3500 cm^-1范围内的红外光谱. 通过比较实验光谱和理论模拟光谱确定了HC_2nO⁺正离子具有端接氢和氧的直线型碳链衍生物结构,基态为三重态,单重态比三重基态能量高10∽15 kcal/mol. 成键分析表明HC_2nO⁺中的碳链具有连烯的结构特征.     

基于自洽GW方法的碳化硅准粒子能带结构计算

在多体微扰理论的框架下, 分别采用G₀W₀方法和准粒子自洽GW方法计算3C-SiC和2H-SiC的准粒子能级. 由一个平均Monkhorst-Pack网格点上的准粒子能级和准粒子波函数出发, 结合最局域Wannier函数插值, 得到3C-SiC和2H-SiC的自洽准粒子能带结构. 3C-SiC的价带顶在Γ点, 导带底在X点. DFT-LDA, G₀W₀和准粒子自洽GW给出的3C-SiC间接禁带宽度分别为 1.30 eV, 2.23 eV和2.88 eV. 2H-SiC价带顶在Γ 点, 导带底在K点. 采用DFT-LDA, G₀W₀和准粒子自洽GW方法得到的间接禁带宽度分别为2.12 eV, 3.12 eV和 3.75 eV. 计算基于赝势方法, 对于3C-SiC和2H-SiC的准粒子自洽GW计算给出的禁带宽度均比实验值略大.     

相对论平均场理论对196Pb超形变态的研究

在形变约束的相对论平均场理论框架下, 用TMA, PK1, NL3和NL-SH相互作用对¹⁹⁶Pb的超形变态进行了系统研究. 给出了¹⁹⁶Pb的位能曲线、基态和超形变态的形变以及超形变态退激的激发能. ¹⁹⁶Pb的基态为β₂≈－0.15的扁椭球, 超形变激发态为β₂≈0.60的长椭球, 激发能在4－5MeV之间, 势阱深度在1－2.2MeV之间. 这些结果与最近观测的实验数据符合得非常好, 表明相对论平均场理论能够较好地描述¹⁹⁶Pb超形变转动带带首的能量.     

几种三元过渡金属碳化物弹性及电子结构的第一性原理研究

基于密度泛函理论平面波方法研究了六方WC型Re_xW_1－xC(x=1, 0.25, 0.75, 0),Re_0.5Os_0.5C和Os_0.5W_0.5C的晶体结构、弹性和电子结构性质.研究发现Re_0.25W_0.75C晶体具有优异的弹性性能及稳定性,其剪切模量(312 GPa)超过了所有其他实验合成和     

α模型中不固定多重数下的阶乘矩、粒子数关联矩

利用二维相空间自仿射分形的随机级联α模型,采用蒙特卡罗模拟的方法,研究了阶乘矩､粒子数关联矩在不固定多重数下,对应于多重数相对起伏强度n_f的依赖关系,得到:阶乘矩、粒子数关联矩依赖于多重数相对起伏n_f,但间歇指数一般不依赖于n_f,当n_f较小时这种依赖性得以消除.     

一维新型阶梯函数光子晶体透射特性

研究了阶梯型折射率n₂₂、n₁₁(阶梯分布高度)的大小、对应的分布厚度、不同入射角以及缺陷模对阶梯函数型光子晶体透射特性的影响.由费马原理给出光在函数光子晶体中的运动方程,再由电磁传播理论给出函数光子晶体的传输矩阵,进一步推导出函数光子晶体的透射率以及电场分布的表达式.研究表明,1)随n₂₂,n₁₁大小或者厚度改变,其禁带变宽;2)随光的入射角增加,其禁带变窄;3)当加入缺陷层时,随着缺陷层介质折射率增加,缺陷模强度减小且位置发生红移;4)在函数光子晶体中,缺陷层前电场分布保持不变,而在缺陷层处以及之后的电场强度都明显增强,这不同于常规光子晶体的电场分布仅在缺陷层处局域增强.     

Spin-weighted spheroidal equation in the case of s=1

We present a series of studies to solve the spin-weighted spheroidal wave equation by using the method of super-symmetric quantum mechanics. We first obtain the first four terms of super-potential of the spin-weighted spheroidal wave equation in the case of s = 1. These results may help summarize the general form for the n-th term of the super-potential, which is proved to be correct by means of induction. Then we compute the eigen-values and the eigen- functions for the ground state. Finally, the shape-invariance property is proved and the eigen-values and eigen-functions for excited states are obtained. All the results may be of significance for studying the electromagnetic radiation processes near rotating black holes and computing the radiation reaction in curved space-time.     

Analytic solutions of the ground and excited states of the spin-weighted spheroidal equation in the case of s=2

By using the super-symmetric quantum mechanics (SUSYQM) method, this paper obtains the analytical solutions for the spin-weighted spheroidal wave equation in the case of s = 2. Based on the derived W 0 to W 4 the general form for the n-th-order super-potential is summarized and is proved correct by mathematical induction. Hence the ground eigenvalue problem is completely solved. Particularly, the novel solutions of the excited state are investigated according to the shape-invariance property.     

The Shape Invariance in <Emphasis Type="Italic">S</Emphasis><Superscript>2</Superscript> Space with Electromagnetic Field

In this paper, we use the Laplace equation in curvature space S ² with electromagnetic field, and write the Schrödinger equation in S ²space. By comparing this equation with well known polynomial we obtain the wave function and energy spectrum. In that case we face with two values of λ which guarantee the stability of system. On the other hand, we take advantage from factorization method, and factorize the second order equation in terms of first order equations. These first orders operators lead us to investigate the potential and super-potential which are satisfied by shape invariance condition. We show that, in order to have such condition the λ must be zero, the energy spectrum also obtained by this condition. Finally we show that these corresponding operators will be generators of algebra.     

Solving the spin-weighted spheroidal wave equation

In this paper we solve spin-weighted spheroidal wave equations through super-symmetric quantum mechanics with a different expression of the super-potential. We use the shape invariance property to compute the ＂excited＂ eigenvalues and eigenfunctions. The results are beneficial to researchers for understanding the properties of the spin-weighted spheroidal wave more deeply, especially its integrability.     

Super-Derivations and Associated Standard Super-Potentials

Abstractly defined super-derivations on Fermionic systems on a lattice are studied. The existence and uniqueness of the associated standard super-potential are shown for every super-derivation with the subalgebra of all local operators as its domain. The relation between the standard super-potential of a super-derivation and the standard potential for the square of the super-potential (which is shown to be a derivation in the case of finite range super-potentials) is obtained (by use of local super-Hamiltonian for the super-derivation and local Hamiltonian for the square). As a consequence, a necessary and sufficient condition for a super-derivation to be nilpotent is obtained in terms of the corresponding standard super potential. Examples of translation invariant nilpotent super-derivations are given in the case of super-potentials of finite ranges on a one-dimensional lattice. A merit of considering the super-potential associated with a super-derivation is that the former can be used as free parameters for the latter.     

Optical analogue of the Aharonov-Bohm effect using anisotropic media

We show that in the context of paraxial optics, which can be analyzed through a wave equation similar to the non-relativistic Schrödinger equation of quantum mechanics but replacing time t by spatial coordinate z, the existence of a vector potential A_⊥ mimicking the magnetic vector potential in quantum mechanics is allowed by specific gauge symmetries of the optical field in a medium with anisotropic refractive index. In this way, we use Feynman?s path integral to demonstrate an optical analogue of the quantum-mechanical Aharonov-Bohm effect, encouraging the search for another optical systems with analogies with more complex quantum field theories.     

The AdS5 Black Hole Space-time with the Perturbed?Dilaton Field Background

The AdS ₅ black hole space-time with perturbed dilaton field background considered. We use the holographic AdS/QCD soft-wall model to investigate the wave functions and the effective potential. In this model, glueballs are described by a massless scalar field in an AdS ₅ black hole with a dilaton soft-wall background. For the first time we use modified dilaton field and discuss the consequence of the perturbation. In order to obtain the effective potential we rewrite the equation of motion in the Schr?dinger like equation, then try to find corresponding solution.     

具有阻尼项的非线性波动方程的相似约化

利用Clarkson和Kruskal引入的直接约化法,给出了具有阻尼项的非线性波动方程u_tt-2bu_xxt+αu_xxxx=β(uⁿ_x)x(α>0,β≠0,n≥2)三种类型的相似约化.从这些约化方程的Painlevé分析表明该方程在Ablowitz的猜测意义下是不可积的.此外还获得了该方程(n=2)的4种精确类孤波解. 关键词： 波动方程 相似约化 Painlevé分析 精确解     

双折射晶体中旋光效应的耦合波理论

与传统的旋光效应理论不同，采用三阶赝张量κ⁽²⁾_jkl描述旋光现象，并将相关的电极化强度作微扰处理，直接从Maxwell方程组出发推导出了双折射晶体中自然旋光效应的耦合波方程组并得到解析解.该解析解包含了已有的旋光效应宏观理论结果，可方便地用于描述任意偏振态的单色光波在任意点群的双折射旋光晶体中沿任意方向的传播行为.最后，以石英晶体为例,通过对出射光波的偏振态分析，研究了波矢失配对旋光效应的影响. 关键词： 耦合波理论 旋光效应 非线性光学     

Some extensions on the soliton solutions for the Novikov equation with cubic nonlinearity

In this paper, by using the bifurcation method of dynamical systems, we derive the traveling wave solutions of the nonlinear equation UU_τyy ? U_yU_τy + U²U_τ + 3U_y = 0. Based on the relationship of the solutions between the Novikov equation and the nonlinear equation, we present the parametric representations of the smooth and nonsmooth soliton solutions for the Novikov equation with cubic nonlinearity. These solutions contain peaked soliton, smooth soliton, W-shaped soliton and periodic solutions. Our work extends some previous results.