Coordinate-Momentum Intermediate Representation and Marginal Distributions of Quantum Mechanical Bivariate Normal Distribution

We introduce bivariate normal distribution operator for state vector [ψ） and find that its marginal distribution leads to one-dimensional normal distribution corresponding to the measurement probability ｜λ,v〈x｜.ψ〉｜^2, where ｜x〉λ,v is the coordinate-momentum intermediate representation. As a by-product, the one-dimensional normal distribution in statistics can be explained as a Radon transform of two-dimensional Gaussian function.     

Evidences of dense Kondo behaviour in the U-Au system: Electrical and magnetic investigations in U14Au51 and UAu2

U₁₄Au₅₁ and UAu₂ were recently demonstrated the two correct phases stable at room temperature in the U-Au system. Magnetic susceptibility (1.5–300 K) and electrical resistivity (10–800 K) measurements were performed in samples of both phases. Magnetic susceptibility temperature behaviour gives evidences of an antiferromagnetic transition at 23 K in U₁₄Au₅₁, whereas no magnetic order is detected in UAu₂. In both compounds, Kondo-like logarithmic behaviour in electrical resistivity temperature trend is found. Effects already observed in U₂Zn₁₇ and UAl₂ are respectively found in U₁₄Au₅₁ and UAu₂. Possible “heavy fermion” properties of these compounds are discussed.     

水下翼型结构流噪声实验研究

为测量流激水下翼型结构的流噪声,提出了一种混响箱测量方法。在重力式水洞中搭建了一套实验测量系统,利用混响箱法测量了水下翼型结构模型的辐射声功率。在此基础上研究了流速及结构参数(厚度、肋、声学覆盖层)对其辐射声功率的影响。结果表明:当流速小于5 m/s时,辐射声功率随流速的6次方增长,符合偶极子的辐射规律;当流速大于5 m/s时,辐射声功率随流速的10土1次方规律增长,不再按偶极子的规律辐射;若对水下翼型结构模型加厚、加环肋及外部敷设黏弹性材料,均可在一定程度上抑制流噪声。此研究方法可对水下复杂结构的辐射声功率测量及结构优化设计提供一定的参考。      

Magnetic and transport properties of some U3T3X4-compounds (T = Co, Ni, Cu and X = Sb, Sn)

We have prepared and studied a new series of isostructural U₃T₃X₄-compounds with T = Co, Ni, Cu for X = Sb and T = Ni for X = Sn. Ferromagnetism is found for U₃Co₃Sb₄ and U₃Cu₃Sb₄ below 10 and 88 K, respectively. In contrast, no magnetic order was observed down to 1.7 K for the semiconductor U₃Ni₃Sb₄ and the “moderately” heavy-fermion system U₃Ni₃Sb₄.     

含特异材料光子晶体隧穿模的偏振特性

构造了由普通材料A(SiO₂)和电单负材料B组成的(AB)^N(BA)^N型一维光子晶体.数值计算表明原禁带的1907.3 nm处出现了一个十分尖锐的隧穿模. 入射角增加,该隧穿模的透射率和半峰全宽度均保持不变,但位置发生蓝移, 入射角在15°-65°的区间内,移动率的绝对值 |dλ/dθ| 较大.当B介质的磁导率μ_B 从5增加到10时,只是隧穿模的位置发生了红移. 介质的几何厚度增加时,隧穿模的透射率不变,但其位置红移明显,半峰全宽略有增加.     

|m| Partial wave treatment for two-dimensional Coulomb-scattering and Regge pole

1 Introduction Though one-dimensional (1D) systems may clearly exhibit many features of quan-tum mechanics, systems with many degrees of freedom provide more opportunities tostudy many other important features, e.g. the degeneracy of energy eigenstates, whichneed a complete set of commuting observables to characterize an energy eigenstate. Inparticular, two-dimensional (2D) systems with two spatial degrees of freedom may ex-hibit symmetries not present in 1D systems, e.g. the rotational symme…     

Stereodynamics study of the H′（^2S） ＋ NH（X^3∑-） 〉 N（4S） ＋ H2 reaction

The stereodynamics and reaction mechanism of the H′（^2S） ＋ NH （X^3∑^-） → N（^4S） ＋ H2 reaction are thoroughly studied at collision energies in the 0.1 eV-1.0 eV range using the quasiclassical trajectory （QCT） on the ground 4A″ potential energy surface （PES）. The distributions of vector correlations between products and reagents P（φr）, P（φr） and P（φr,φr） are presented and discussed. The results indicate that product rotational angular momentum j′ is not only aligned, but also oriented along the direction perpendicular to the scattering plane; further, the product H2 presents different rotational polarization behaviors for different collision energies. Furthermore, four polarization-dependent differential cross sections （PDDCSs） of the product He are also calculated at different collision energies. The reaction mechanism is analyzed based on the stereodynamics properties. It is found that the abstraction mechanism is appropriate for the title reaction.     

Energy excitations in three-axial magnets with single-ion and exchange anisotropies

The energy spectra of three-axial ferromagnets like U₃P₄ and ferrimagnets like U₃Sb₄ are presented and their properties are discussed. In case of U₃Sb₄ we find an interesting example of a magnetic structure which, due to the single-ion anisotropy, is unstable in the spin wave approximation. The k² dependence of magnon energies requires re-examination of the temperature dependence of the magnetisation and of the specific heat.     

On Diagonal P-Representation of Superposition Field of Two Light Modes

For the superposition field a₁^†+a₂^† of two light modes we introduce an appropriate diagonal P-representation which is constructed on the common eigenvectors |z,x〉of (X₁-X₂) and a₁+a₂, where X_i=(a_i+ a_i^†)/√(2), [a_i,a_i^†] =δ_ij. It is remarkable that |z,x〉make up a new quantum mechanical representation.     

Complex Wavelet Transform of the Two-mode Quantum States

By employing the bipartite entangled state representation and the technique of integration within an ordered product of operators, the classical complex wavelet transform of a complex signal function can be recast to a matrix element of the squeezing-displacing operator U ₂(μ, σ) between the mother wavelet vector 〈ψ| and the two-mode quantum state vector |f〉 to be transformed. 〈ψ|U ₂(μ, σ)|f〉 can be considered as the spectrum for analyzing the two-mode quantum state |f〉. In this way, for some typical two-mode quantum states, such as two-mode coherent state and two-mode Fock state, we derive the complex wavelet transform spectrum and carry out the numerical calculation. This kind of wavelet-transform spectrum can be used to recognize quantum states.     

基于4A"势能面研究C(3P)+NO(X2Π)→CO(X1Σ+)+N(4S)反应的立体动力学性质

运用准经典轨线方法(QCT), 基于Abrahamsson等构造的⁴A"势能面(Abrahamsson E Andersson S, Nyman G, Markovic N 2008 Phys. Chem. Chem. Phys. 10 4400), 在碰撞能为0.06 eV时, 对C(³P)+NO(X²Π )→CO(X¹Σ⁺)+N(⁴S)反应立体动力学性质进行了理论研究. 在考虑反应物NO转动和振动激发的条件下, 计算了质心坐标系下k-j'矢量(k与j'分别为反应物速度与产物角动量)相关的P(θ_r)分布和k-k'-j'矢量(k'为产物相对速度)相关的P(φ_r)分布. 此外还计算了该反应的三个极化微分截面(2π/σ)(dσ₀₀/dω_t), (2π/σ)(dσ₂₀/dω_t)以及(2π/σ)(dσ₂₂+dω_t). 计算结果表明转动和振动激发对产物取向影响较大而对定向影响较小; 对于三个极化微分截面, 转动激发的影响不大, 而振动激发的影响则较大.     

Quasi-classical trajectory study of the isotope effect on the stereodynamics in the reaction H(2S)+CH(X2Π; v=0, j=1)→C(1D)+H2(X1Σg+)

The isotope effect on the stereodynamic properties in the title reaction is investigated by a quasi-classical trajectory (QCT) method on the 1¹A' potential energy surface at a collision energy of 23.06 kcal/mol. The angular distributions P(θ_r), P(ø_r), P(θ_r, ø_r), and the polarization-dependent generalized differential cross sections are calculated, which demonstrate the observable influences on the rotational polarization of the product by the isotopic substitution of H with D.     

Effects of collision energy and rotational quantum number on stereodynamics of the reactions:H(~2S)+NH(v=0,j=0,2,5,10)→N(~4S)+H_2

The stereodynamical properties of H(~2S) + NH(v = 0,j = 0,2,5,10)→N(~4S) + H_2 reactions are studied in this paper by using the quasi-classical trajectory(QCT) method with different collision energies on the double many-body expansion(DMBE) potential energy surface(PES)(Poveda L A and Varandas A J C 2005 Phys.Chem.Chem.Phys.7 2867).In a range of collision energy from 2 to 20 kcal/mol,the vibrational rotational quantum numbers of the NH molecules are specifically investigated on v = 0 and j = 0,2,5,10 respectively.The distributions of P(θ_r),P(φ_r),P(θ_r,φ_r),(2π/σ)(dσ_(00)/dω_t)differential cross-section(DCSs) and integral cross-sections(ICSs) are calculated.The ICSs,computed for collision energies from 2 kcal/mol to 20 kcal/mol,for the ground state are in good agreement with the cited data.The results show that the reagent rotational quantum number and initial collision energy both have a significant effect on the distributions of the k-j',the k-k'-j',and the k-k' correlations.In addition,the DCS is found to be susceptible to collision energy,but it is not significantly affected by the rotational excitation of reagent.     

色散方程的一类具任意稳定性的显格式

本文对色散方程u_r=au_xxx构造了一类中间层包含四个结点,带两个参数m和θ的三层显式差分格式。当m和θ满足一定的关系时,其稳定性条件为|γ|≤(m+1)/(4(m-1))(|m|>1),从而当取m充分接近1时,可得到任意大的稳定性条件,并且保持截断误差阶不变。数值例子验证了理论分析的结果。     

COMPACTIFICATION FROM E8 × E8 TO THE STANDARD MODEL

The comnactification of the D=10 E₈ × E₈ field theory limit of superstring to the D=4 SU₃ × SU₂ × U₁ standard model is investigated by means of the scheme developed by Manton, Forgacs and Chapline.     

βγ(CP) correlation measurements and anti-analogue structure in the decay of Ca

β-γ(CP) correlation measurements have been carried out on the sequence in the decay of the ground state of ⁴⁹Ca to the (presumed) anti-analogue state at 3.105 MeV excitation in ⁴⁹Sc. An asymmetry parameter of A = −0.132 ± 0.017 was obtained, making any spin-parity assignment other than very unlikely for the 3.105 MeV state. The deduced Fermi matrix element for the decay is |M_{v| = |1.4 ± 9.7| × 10⁻³}, which leads to an isospin impurity ( ) corresponding to the mixing of the analogue state (at 11.6 MeV) and the 3.105 MeV state of ||² 1.6 × 10⁻⁵. This leads in turn to an effective Coulomb matrix element of |H_c| = |3.9 ± 27.4| keV, a low value compared to the value of 100 keV obtained from a theoretical estimate based on simple shell-model wave functions for the single-particle states involved.     

CONFINEMENT PROPERTIES OF THE PURE GAUGE FIELDS ON COSET SPACE OF AN ABELIAN CHIRAL GROUP

In this paper the lattice current-current propagator is calcdlated and the influence of coset pure gauge fields of an abelian chiral group G=U₁×U₁⁵ on confinement properties of a quark system is discussed by virtue of the Wilson's criterion in lattice gauge theory. When subgroup H is U₁, the coset pure gauge fields only contribute a perimeter law factor to the current current propagator which has no influence on confinement properties of the system. When subgroup H is U_s, the coset puregauge fields have no influence on wnfinement properties of the system either.     

Vibrational Spectra and Potential Energy Surface for Electronic Ground State of Jet-Cooled Molecule S2O

The vibration states of transition molecule S₂O, including both bending and stretching vibrations, are studied in the framework of dynamical symmetry groups U₁(4)\otimes U₂(4). We get all the vibration spectra of S₂O by fitting 22 spectra data with 10 parameters. The fitting rms of the Hamiltonian is 2.12 cm^-1. With the parameters and Lie algebraic theory, we give the analytical expression of the potential energy surface, which helps us to calculate the dissociation energy and force constants of S₂O in the electronic ground state.     

Deformation of Superoperator's Kraus Representation Derived by Weyl Correspondence and Entangled State Representation

By virtue of the Weyl correspondence and based on the the technique of integration within an ordered product of operators, we show under what condition the superoperator's Kraus representation ρ^ˊ=∑_μ A_μρA_μ^† can be deformed as ρ^ˊ=(1/π)∫d²αB(α)D(α)ρD^†(α), where D(α) is the displacement operator, B(α) is a probability density related to the classical Weyl correspondence of A_μ. An alternate discussion by using the entangled state representation and through a quantum teleportation process is also presented.     

ZnAl2O4:Cr3+晶体4A2基态ZFS及其三角晶格畸变研究

用对角化哈密顿矩阵的方法,借助New man晶场叠加模型,研究了ZnAl₂O₄:Cr³⁺晶体的基态零场分裂(ZFS)及其电子光谱,理论结果与实验一致.定量研究表明,掺杂晶体ZnAl₂O₄:Cr³⁺中,络离子(CrO₆)^9-局域结构应有压缩的三角畸变(△θ=3.06°).同时指出,自旋二重态对⁴A₂基态ZFS参量b₂⁰的贡献不可忽略,而对g因子的贡献甚微.