一类相空间中的准几率分布函数系

定义了一类相空间中的准几率分布函数系，这个准几率分布函数系直接建立在具有更加广泛意义的量子相空间Schr?dinger方程解的基础之上，其中定义_α=αp-i?q和_α=(1-α)q+i?p.发现了两个有趣的关系.(1)建立的量子相空间Schr?dinger方程的解实际上是对函数φ(λ)exp［i(1-α)qp］做窗口Fourier变换.(2)这个窗口函数g(λ)起着选择窗口形式的作用，而且不同的窗口对应着不同的分布函数.当g(λ)是一个代表Gauss窗的Gauss函数的时候，准几率分布函数就是一个类似于Husimi的分布函数f^HL_α(q,p)；当g(λ)是一个表示椭圆的复函数时，准几率分布函数就是一个椭圆分布函数f^E_α(q,p)；再在g(λ)为复函数的基础上附加α=0，就可得到标准序分布函数f^S(q,p)、反标准序分布函数f^AS(q,p)和Wigner分布函数f^W(q,p)，此时g(λ)表示高度为1/12π?而长度为λ的矩形窗. 关键词： 窗口Fourier变换 相空间 Wigner分布函数     

径向积分的解析计算

本文阐明的方法能方便地求出径向积分ⁿ₁^l₁F_Lⁿ₂^l₂(q)≡∫₀^∞> (R_n1^l₁(αr)jL(Kr)R_n2^l₂(αr)r²dr(q≡(K)/(α))的解析表达式。文中给出了L=0,1,2情况下各个径向积分的解析式,同时还以多重求和的形式络出了对各种量子数L,n₁,l₁,n₂,l₂适用的径向积分表达式。     

基于幂次相互作用的二维磁性团簇耦合能研究

在扩散限制凝聚模型基础上,采用Monte Carlo方法模拟了磁耦合作用随粒子间距离幂次变化的磁性粒子动力学凝聚过程.重点研究了在不同幂指数α值下团簇在生长过程中,即随着粒子数N的增加,团簇平均耦合能E_c(N)的演化过程.模拟结果表明:对于α≥5时,E_c(N)随着粒子数N的增加变化较小;当α=2时,E关键词： 扩散限制凝聚模型 幂次相互作用 耦合能     

中低能非全裸C离子与He原子的碰撞研究

采用反冲离子飞行时间-散射离子位置灵敏符合测量技术，测量了能量范围在0.7v₀—4.4v₀(v₀为玻尔速度)的碳离子C^q+(q=1—4)与He原子碰撞过程不同出射道靶原子的双电离与单电离截面比R，包括入射离子不损失电子(直接电离)的出射道(R_q,q),入射离子俘获一个电子的出射道(R_q,q-1)和入射离子损失一个电子的出射道(R_q,q+1)，并研究了R随入射C离子的能量及电荷态的变化关系.实验表明，对给定电荷态的入射离子，靶原子的双电离与单电离截面比R与出射道有很强的依赖关系，即R_q,q<R_q,q+1<R_q,q-1.直接电离出射道截面比R_q,q与入射离子电荷态几乎无关，而入射离子俘获一个电子的出射道和损失一个电子的出射道靶原子双电离与单电离截面比R_q,q-1和R_q,q+1却与入射离子电荷态有很强的关系.采用原子极化理论和电子屏蔽与反屏蔽作用对实验结果进行了解释. 关键词： 离子-原子碰撞 电离 截面比     

非对称量子点中磁极化子性质的磁场和温度依赖性

采用Tokuda线性组合算符法和Lee-Low-Pines变换法,研究了温度和磁场对非对称抛物量子点中强耦合磁极化子性质的影响,简捷地得到了作为量子点的横向受限强度ω₁、纵向受限强度ω₂、电子-声子耦合强度α、外磁场的回旋频率ω_c和温度参数γ的函数的磁极化子的振动频率λ、基态能量E₀和有效质量m 关键词： 非对称量子点 强耦合磁极化子 磁场和温度依赖性     

高阶Adams公式的系数

当k的值不大时(例如k≤4),诸系数γiγi^*,β_kρ,β_kρ^*易于手工计算。但对大的k值(例如k≥5),手工计算已非易事。利用著名的计算机代数软件:REDUCE^[a],我们可以很容易地计算出诸系数γi,γi^*,β_kρ,β_kρ^*。     

关于MgB2/Al2O3超导薄膜电阻转变和各向异性的研究

利用电子束蒸发方法将MgB₂超导薄膜沉积到Al₂O₃(001)衬底上.采用标准的四引线法研究了磁场平行和垂直超导薄膜ab平面下的电阻转变.一个激活能模型 U(T,H)=U₀(1-T/(T_c+δ))ⁿ(1-H/H 关键词： 2/Al₂O₃')" href="#">MgB₂/Al₂O₃ 超导体 电阻转变 各向异性     

模糊聚类正交方法若干结果

本文提出一个新的模糊聚类方法:正交法,这种方法基于如下正交聚类原则:记截矩阵R_λ=(α₁,α₂,…,α_n),其中列向量α_j=(α_1j,α_2j,…,α_nj)^T,所谓向量α_i,α_j正交,指内积(α_i,α_j)=0。     

褶积反演中的脉冲压缩准则

通过分析基于脉冲压缩原理的反褶积方法,提出了具有广泛用途的广义L_p模准则,像脉冲反褶积、极小熵反褶积、L₁模反褶积和D模反褶积等都为其特例。根据有限维欧氏空间的L。模性质和高维欧氏空间的几何性质,分析了广义L_p模方法中的参数影响。为了比较不同反褶积方法的脉冲压缩效果,给出了一类判别函数,从理论上证明了,为什么对非小相位信号L₁模法的脉冲压缩效果优于脉冲反褶积;D模反褶积要比常规极小熵法更具有"简单性"。广义L_p模准则为构造、分析新的反褶积方法和进一步研究最优脉冲压缩准则提供了必要的理论基础。     

Dynamic models of pest propagation and pest control

This paper proposes a pest propagation model to investigate the evolution behaviours of pest aggregates. A pest aggregate grows by self-monomer birth, and it may fragment into two smaller ones. The kinetic evolution behaviours of pest aggregates are investigated by the rate equation approach based on the mean-field theory. For a system with a self-birth rate kernel I(k)=Ik and a fragmentation rate kernel L(i,j)=L, we find that the total number M₀^A(t) and the total mass of the pest aggregates M₁^A(t) both increase exponentially with time if L ≠ 0. Furthermore, we introduce two catalysis-driven monomer death mechanisms for the former pest propagation model to study the evolution behaviours of pest aggregates under pesticide and natural enemy controlled pest propagation. In the pesticide controlled model with a catalyzed monomer death rate kernel J₁(k)=J₁k, it is found that only when I<J₁B₀ (B₀ is the concentration of catalyst aggregates) can the pests be killed off. Otherwise, the pest aggregates can survive. In the model of pest control with a natural enemy, a pest aggregate loses one of its individuals and the number of natural enemies increases by one. For this system, we find that no matter how many natural enemies there are at the beginning, pests will be eliminated by them eventually.     

准周期层状铁磁超晶格的实空间重整化群方法

本文用实空间重整化群方法讨论了准周期层状铁磁超晶格的磁自旋波,用Reduce语言推导了decimation变换公式,从而求得了局域格林函数、局域态密度和约化磁矩。发现局域态密度的带宽和约化磁矩与最近邻相互作用J₁、J₂及格点自旋s_a、s_b密切相关。     

NFX(X=-1,0,+1)分子离子基态的结构与势能函数

用密度泛函理论的B3LYP方法,分别以6-311++g(df,3pd),6-311g(3d,3p)和6-311++g(3df,3pd)为基函数对NF分子、NF⁺和NF^-离子基态进行几何优化和频率计算,并进行单点能扫描计算.用最小二乘法拟合得到NF^X(X=-1,0,+1)分子离子基态的Murrell-Sorbie势能函数.利用得到的解析势能函数计算出的NF分子和NF⁺离子基态光谱常数(B_e,α_e,ω_e,ω_eχ_e)与实验值符合很好.首次得到NF^-离子基态的光谱常数(B_e,α_e,ω_e,ω_eχ_e)和力常数(f₂,f₃,f₄),为NF-离子基态的后期研究提供理论参考.     

SeN_2自由基解析势能函数的耦合簇理论研究

利用单双迭代耦合簇理论CCSD结合相关一致四重基组cc-pVQZ对SeN2基态的平衡结构和谐振频率进行了优化计算.计算结果表明:基态SeN2自由基分子稳定态为C2v构型,基态电子组态为X1A1,平衡核间距RSe-N=0.1691 nm,RN-N=0.1970 nm,αN-Se-N=71.289?,离解能De=4.78 eV.基态简正振动频率分别为:ν1=326.9288 cm-1,ν2=808.0161 cm-1以及ν3=948.3430 cm-1.对SeN基态和N2基态采用上述相同方法进行几何构型与谐振频率的计算并进行单点能扫描,使用Murrell-Sorbie函数进行最小二乘拟合得到其势能函数和光谱常数,通过和其他理论值以及实验值做比较,显示本文的计算工作达到了很高的精度.应用多体项展式理论导出了基态SeN2的全空间解析势能函数,其势能函数等值势能图准确再现了SeN2分子的结构特征和能量变化.     

Monte Carlo optimisation of correlated wave functions for normal two-electron systems

A simple, new type of correlated wave function is proposed for the studies of normal two-electron atomic systems: ψ(r₁, r₂) = Σc_mΦ_m(r₁, r₂) with Φ_m(r₁, r₂) = exp[−(r₁ + r₂)]/(br₁₂ + a)^m, where , a, b are non-linear variational parameters. A notable feature of this basis function is that only three terms are required within the framework of the Raleigh-Ritz variational principle to obtain fairly accurate energy eigenvalues and satisfactory cusp conditions. The non-linear variational parameters are optimised by using the Monte Carlo technique.     

Interprétation de la susceptibilité magnétique de l'oxysulfure de samarium par un modèle de champ cristallin

The paramagnetic susceptibility of polycrystalline samarium oxysulfide has been measured between 3° and 300°K. The data are interpreted with an approximation to the crystal potential of the form

V_c = _JV₂⁰O₂⁰ + β_JV₄⁰O₄⁰ + β_JV₄³O₄³

and correction taking into account exchange is made. The energy levels and crystal fields parameters have been calculated. Fluorescence studies of Gd₂O₂S: Sm³⁺ and Y₂O₂S: Sm³⁺ have confirmed these results.     

Cu1-xHxZr2(PO4)3中Cu2+的EPR谱和局域结构研究

本文采用Cu²⁺斜方对称电子顺磁共振（EPR）参量的高阶微扰公式计算了晶体Cu_1-xH_xZr₂（PO₄）₃中Cu²⁺的EPR参量（g因子和超精细结构常数A因子）．计算结果表明,晶体Cu_1-xH_xZr₂（PO₄）₃中[CuO₆]^10-基团的Cu-O键长分别为R_||≈0.241 nm,R_⊥≈0.215 nm,平面键角τ≈80.1°;由于对称性降低,中心金属离子基态²A_1g（θ）和²A_1g（ε）有一定程度混合,混合系数α≈0.995．所得EPR谱图的理论计算值与实验数据符合得很好．     

相位角对容性耦合电非对称放电特性的影响

电非对称效应作为一种新兴技术,被广泛用于对离子能量和离子通量的独立调控.此外,在改善等离子体的径向均匀性方面,电非对称效应也发挥了重要作用.本文采用二维流体力学模型,并耦合麦克斯韦方程组,系统地研究了容性耦合氢等离子体中当放电由多谐波叠加驱动时,不同谐波阶数k下的电非对称效应,重点观察了相位角θ_n对自偏压以及等离子体径向均匀性的影响.模拟结果表明：在同一谐波阶数下,自偏压随相位角θ_n的变化趋势不尽相同,且当k增大（k>3）时,自偏压随最高频相位角θ_k的变化范围逐渐减小.此外,通过调节相位角θ_n,可以改变轴向功率密度和径向功率密度的相对关系,进而实现对等离子体径向均匀性的调节.研究结果对于利用电非对称效应优化等离子体工艺过程具有一定的指导意义.     

Ultrafast structural dynamics using time-resolved x-ray diffraction driven by relativistic laser pulses

Based on a femtosecond laser plasma-induced hard x-ray source with a high laser pulse energy( 100 mJ) at 10 Hz repetition rate,we present a time-resolved x-ray diffraction system on an ultrafast time scale.The laser intensity is at relativistic regime(2 × 10~(19) W/cm~2),which is essential for effectively generating K_α source in high-Z metal material.The produced copper K_α radiation yield reaches to 2.5 × 10~8 photons/sr/shot.The multilayer mirrors are optimized for monochromatizating and two-dimensional beam shaping of K_α emission.Our experiment exhibits its ability of monitoring the transient structural changes in a thin film SrCoO_(2.5) crystal.It is demonstrated that this facility is a powerful tool to perform dynamic studies on samples and adaptable to the specific needs for different particular applications with high flexibility.     

Abnormal breakdown of Stokes–Einstein relation in liquid aluminium

We present the results of systematic molecular dynamics simulations of pure aluminium melt with a well-accepted embedded atom potential. The structure and dynamics were calculated over a wide temperature range, and the calculated results(including the pair correlation function, self-diffusion coefficient, and viscosity) agree well with the available experimental observations. The calculated data were used to examine the Stokes–Einstein relation(SER). The results indicate that the SER begins to break down at a temperature T_x(~1090 K) which is well above the equilibrium melting point(912.5 K).This high-temperature breakdown is confirmed by the evolution of dynamics heterogeneity, which is characterised by the non-Gaussian parameter α_2(t). The maximum value of α 2(t), α_(2,max), increases at an accelerating rate as the temperature falls below Tx. The development of α_(2,max) was found to be related to the liquid structure change evidenced by local fivefold symmetry. Accordingly, we suggest that this high-temperature breakdown of SER has a structural origin. The results of this study are expected to make researchers reconsider the applicability of SER and promote greater understanding of the relationship between dynamics and structure.