各向同性谐振子径向矩阵元的通项表达式

推导出三维各向同性谐振子径向矩阵元p|n′l′>和二维各向同性谐振子径向矩阵元q|n′m′>的通项表达式- 关键词：     

相对论性无自旋氢原子的径向矩阵元的递推关系

导出相对论性无自旋氢原子的径向矩阵元〈nl|rp|n′l′〉的递推关系.     

氢原子基下径向矩阵元的递推关系

推导出氢原子基下径向矩阵元〈nl|rk|n′l′〉所满足的递推关系.     

m维氢原子径向矩阵元的通项计算公式

给出了n维氢原子的归一化径向波函数,推导出了n维氢原子的任意径向矩阵元〈NJ|rq|N′J′〉的通项计算公式。     

一维Morse势动量算符矩阵元的通项公式

导出一维Morse势中动量算符矩阵元〈n|Ap^G2q|n′〉的通项计算公式.     

谐振子径向幂坐标矩阵元的一般递推关系

利用谐振子径向波函数的渐近行为和积分特性,导出了谐振子径向幂坐标矩阵元〈n′_rl′|r~k|n_rl〉的递推关系,从而把有关文献中关于对角元〈n_rl|r~k|n_rl〉的递推关系推广到更为一般的形式。     

相对论性无自旋氢原子径向矩阵元的通项公式及平均值的解析表达式

给出了相对论性无自旋氢原子的解析波函数,推导出了计算径向矩阵元的通项公式.在-6≤s≤3的条件下,给出了径向平均值〈n′l′|rs|n′l′〉的解析表达式.     

相对论性氢原子径向算符矩阵元的通项计算公式

给出了相对论性氢原子径向算符矩阵元〈n′₁,K₁,j₁,m_j1|r^p|n′₂,K₂,j₂,m_j2〉的通项计算公式. 关键词：     

原子模型势中任意算符矩阵元的递推关系

运用升降算子和超维里定理计算出原子模型势中任意算符Af^U2(r)的矩阵元〈n′1l′1|Af^U2(r)|n1l1〉的递推关系.     

Robust quantum secure direct communication and authentication protocol against decoherence noise based on six-qubit DF state

By using six-qubit decoherence-free(DF) states as quantum carriers and decoy states, a robust quantum secure direct communication and authentication(QSDCA) protocol against decoherence noise is proposed. Four six-qubit DF states are used in the process of secret transmission, however only the |0′〉 state is prepared. The other three six-qubit DF states can be obtained by permuting the outputs of the setup for |0′〉. By using the |0′〉 state as the decoy state, the detection rate and the qubit error rate reach 81.3%, and they will not change with the noise level. The stability and security are much higher than those of the ping–pong protocol both in an ideal scenario and a decoherence noise scenario. Even if the eavesdropper measures several qubits, exploiting the coherent relationship between these qubits, she can gain one bit of secret information with probability 0.042.     

稠苯芳杂环及其烷基质子化学位移的计算

本文提出了予测稠苯芳杂环及其烷基链上质子化学位移的计算方法。 将稠苯芳杂环化合物用凯库勒式表示,计算式为为需考虑的苯环内的乙烯基效应。σ_mi,ci为各苯环的环流效应。σ_1,Hc为各芳杂环的屏蔽效应,对杂环上质子它就是该单独芳杂环上相应质子的δ值,对苯环上质子要将它分解为各结构因素的效应,即:σ_1,He=(1/2)^d-1δ_x=y(或σ_z)+σ_c-c·σ_m,H. σ_x-y与σ_z为杂原子或其基团的屏蔽效应,σ_c=c为存在于芳杂环中的乙烯基的效应,σ_m,Hc为芳杂环的环流效应,d为对不同质子所考虑的键数。有取代基时需考虑取代基的效应。计算环上烷基质子的公式为:δ=σ_p,CH3+ασ_c,CH3+βσ_t,CH3+σ_l,G σ_l,G为稠苯芳杂环基的某级效应。     

Structural phase transitions at clean and metal-covered Si(111) surfaces investigated by RHEED spot analysis

Structural phase transitions between various kinds of superlattice structures formed on a Si(111) surface have been investigated by spot analysis of reflection high-energy electron diffraction (RHEED). Reversible transitions induced by temperature changes and irreversible ones induced by metal depositions were observed. Detailed discussions on the dynamics of the phase transitions are made by quantitative analyses of integrated spot intensity and profile. For a phase transition of 7′7  1′1 structures on a clean Si(111) surface, a hysteresis with temperature difference of 5°C. between in heating and cooling processes was found in the spot intensity change, indicating a first-order transition. Hysteresis was hardly recognized, on the other hand, for transitions of Au-induced superstructures (5×2-Au or ×-Au)  1×1-Au. The spot profiles were found to be broadened during the transition of Si(111)-×-Au  1×1-Au, which was a signature of a continuous transition, while the profiles remained unchanged during the transitions of the 7×7  1×1 and 5×2-Au  1×1-Au phases. Structural conversions induced by In adsorption on the Si(111) surface kept at constant temperatures were also analyzed. The conversions at room temperature were totally dependent on the initial substrate surface structures; the 7×7 surface did not show any structural conversion with In adsorption, while the ×-In surface successively converted to a 2×2 and a × phase with coverage increase. The structural transitions at elevated temperatures were sensitively dependent on the temperatures. Sequences of transitions among the 7×7, 4×1, ×, 1×, and ×4 were quantitatively revealed as changes in RHEED spot intensity.     

ErP5O14非晶玻璃的红外量子剪裁

研究了Er_1.0P₅O₁₄铒非晶玻璃的红外量子剪裁现象. 从吸收谱和激发光谱的计算比较中肯定了Er_1.0P₅O₁₄非晶 玻璃的1537.0 nm红外荧光为多光子量子剪裁荧光. 从Er_1.0P₅O₁₄非晶玻璃的可见和红外荧光发射光谱中发现激发²H_11/2, ⁴G_11/2和⁴G_9/2能级所导致的⁴I_13/2→⁴I_15/2量子剪裁红外荧光很强;基于自发辐射速率、无辐射弛豫速率和能量传递速率等参数的计算,对其量子剪裁机理进行了分析.发现起源于基态的强下转换能量传递{²H_11/2→⁴I_9/2,⁴I_15/2→⁴I_13/2},{⁴G_11/2→⁴I_13/2, ⁴I_15/2→²H_11/2},{⁴G_9/2→⁴F_7/2,⁴I_15/2→⁴I_13/2}和{⁴G_9/2→⁴I_13/2, ⁴I_15/2→²H_11/2}是导致Er_1.0P₅O₁₄非晶玻璃具有强的三光子和四光子量子剪裁红外荧光的原因.研究结果对改善太阳能电池效率有一定意义.     

1-forms over the moduli space of irreducible connections defined by the spectrum of Dirac operators

Let (P) be the moduli space of irreducible connections of a G-principal bundle P over a closed Riemannian spin manifold M. Let D_A be the Dirac operator of M coupled to a connection A of P and f a smooth function on M. We consider a smooth variation A(u) of A with tangent vector ω and denote T_ω:= (D_A(u)−f) (u=0. The coefficients of the asymptotic expansion of trace (T_ω · e^-t(D_A−f)2) near t=0 define 1-forms a^(k)_f, K=0, 1, 2, … on (P). In this paper we calculate aa⁽⁰⁾_f, a⁽¹⁾_f, a⁽²⁾_f and study some of their properties. For instance using the 1-form a⁽²⁾_f for suitable functions f we obtain a foliation of codimension 5 of the space of G-instantons of S⁴.     

Phase formation and magnetic properties of Nd2Fe14B-type Nd16Co76B8−xCx alloys and their hydrides

An attempt is made to synthesize Nd₂Co₁₄C compound by mechanical alloying Nd₁₆Co₇₆B_8−xC_x (0x8) alloys and subsequent annealing. Phase formation and magnetic properties of Nd₂Fe₁₄B-type Nd₁₆Co₇₆B_8−xC_x alloys and their hydrides are investigated. The Nd₂Co₁₄(B,C) phase with Nd₂Fe₁₄B-type structure is formed for Nd₁₆Co₇₆B_8−xC_x (0x7) alloys, while NdCo₇C_δ phase with TbCu₇-type structure is observed in Nd₁₆Co₇₆C₈ alloy. The lattice parameter c of the Nd₂Co₁₄(B,C) phase decreases with increasing the carbon content. A limit volume of the unit cell to form the Nd₂Fe₁₄B-type structure is estimated to be 0.870 nm³. The spin-reorientation temperature T_SR increases with increasing the carbon content, due to an enhancement of magnetocrystalline anisotropy caused by carbon substitution for boron. After hydrogenation, the lattice expansion is observed for Nd₁₆Co₇₆B_8−xC_x (0x7) alloys. The spin-reorientation temperature of Nd₁₆Co₇₆B_8−xC_xH_y (0x7) is much lower than that of the host alloys. Some structural and magnetic properties of hypothetic Nd₂Co₁₄C and Nd₂Co₁₄CH_y compounds are estimated by extrapolation.