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.     

New Approach for Calculating Tomograms of Quantum States by Virtue of the IWOP Technique

We show that for tomographic approach there exist two mutual conjugate quantum states [p,σ, τ） and [x,μ, ν） （named the intermediate coordinate-momentum representation）, and the two Radon transforms of the Wigner operator are just the pure-state density matrices [p）σ1τσ1τ （p｜ and （p）λ,ν,λ,ν,（x｜ respectively. As a result, the tomogram of quantum states can be considered as the module-square of the states＇ wave function in these two representations. Throughout the paper we fully employ the technique of integration within an ordered product of operators. In this way we establish a new convenient formalism of quantum tomogram.     

Application of Fourier Slice Theorem in Wigner Operator Theory and New Complete Representation

By applying the Fourier slice theorem, S_θ(λ) =∫_{-\infty }^{\infty }P_θ(t)e^-iλt=F(λcosθ,λsinθ), where P_θ(t) is a projection of f( x,p) =∫∫_{-\infty}^{\infty }F( u,v) e^i(ux+vp)ldudv along lines of constant, to the Wigner operator we are naturally led to projection operator (pure state), which results in a new complete epresentation. The Weyl orderimg formalism of the Wigner operator is used in the derivation.     

常温和0.1～1 400 MPa条件下黄铜矿的拉曼光谱研究

实验利用金刚石压腔装置研究了常温和0.1～1 400 MPa范围内黄铜矿A₁振动模式的原位拉曼光谱特征。结果显示在实验条件范围内,该拉曼振动峰的强度和形态保持稳定,表明晶格内Cu-S和Fe-S间的相互作用没有发生质变。实验发现黄铜矿该拉曼振动的波数随着压力升高连续向高频方向移动,两者的线性关系为：ν₂₉₀＝0.031 2p+290.60(0.1≤p<58.8 MPa)和ν₂₉₀＝0.005 72p+292.10(58.8≤p<1 400 MPa)dν/dp。常温下58.8 MPa是黄铜矿该拉曼波数随压力变化率的一个突变点,低于和高于该压力时分别为31.2和5.72 cm-1·GPa-1,显著的差异表明黄铜矿的结构可能发生了某种改变。     

A Kind of Three-Mode Entangled States of Continuum Variables Generated by Beam Splitter and Parametric Down-Conversion Amplifier

In three-mode Fock space we find a new tripartite entangled state |α,γ>_λ, which make up a new quantum mechanical representation. The state |α,γ>_λ can be generated by using the setup composing of a beam splitter and a parametric down-conversion amplifier. Application of the state is briefly discussed.     

New Tripartite Nonlinear Entangled State Representation in Quantum Mechanics

Based on the technique of integral within an ordered product of nonlinear bosonic operators, we construct a new kind of tripartite nonlinear entangled state |α,γ〉_λ in 3-mode Fock space, which can make up a complete set. We also simply discuss its properties and application.     

{Q\bar{s}}{\bar{Q}(') s} Molecular States in QCD Sum Rules

We systematically investigate the mass spectra of {Q\bar{s}}{bar{Q}^(')s}molecular states in the framework of QCD sum rules. The interpolating currents representing the molecular states are proposed. Technically, contributions of the operators up to dimension six are included in operator product expansion (OPE). The masses for molecular states with various{Q\bar{s}} {\bar{Q}^(')s} configurations are presented. The result 4.36±0.08 GeV for the D^*_s\bar{D}^*_s0 molecular state is consistent withthe mass 4350^+4.6_-5.1 ± 0.7 MeV of the newly observed X(4350), which could support X(4350) interpreted as a D^*_s\bar{D^}*_s0 molecular state.     

辽东湾海冰反射特性

海冰反照率是研究海冰表面特性、海冰分布、海冰厚度和极地气候的重要光学量之一。将卫星于不同位置所测量到的海冰双向反射率准确地转化为相应的反照率的值,对于获得大规模海冰的时空特性是非常重要的。研究了辽东湾海冰反照率与海冰双向反射分布函数之间的相关关系。结果表明：(1)反照率与海冰组分密切相关,海冰表层颗粒物浓度越高,反照率α(λ)的值越小,气泡的含量越高,α(λ)越大;(2)当仪器探头天顶角θ为0°时,所测量的双向反射因子R_f与反照率α(λ)的值是相似的;随着θ的增大,R_f的值逐渐增大,且与探头方位角的相关性逐渐增强;当θ的值等于太阳天顶角63°时,R_f的值最大,且与探头方位角的相关性最强;(3)不同类型的冰具有不同的各向异性反射因子。     

Experimentally Determining Bloch Parameters of Hamiltonian for Single-Qubit Systems

By considering the identification problem of unknown but fixed Hamiltonian H = S0σ0 ＋∑i=x,y,z Siσi where σi （i = x, y, z） are pauli matrices and σ0=I, we explore the feasibility and limitation of empirically determining the Hamiltonian parameters for quantum systems under experimental conditions imposed by projective measurements and initialization procedures. It may be unsurprising to physicists that one can not obtain the knowledge of So no matter what kind of projective measurements and initialization are permitted, but the observation draws our attention to the importance of the parameter identifiability under different experimental condition. It has also been revealed that one can obtain the knowledge of ｜Sz｜ and Sx^2＋Sy^2 at most when only the projective measurement {｜0/（0｜, ｜1/（1｜} is permitted to perform on and initialize the qubit. Further more, we demonstrated that it is feasible to distinguish ｜Sx｜, ｜Sy｜, and ｜Sz｜ even without any a priori information about Hamiltonian if at least two kinds of projective measurement or initialization procedures are permitted. It should be emphasized that both projective measurements and initialization procedures play an important role in quantum system identification.     

Four-Particle Entangled State Representation and Its Squeezing Transformation

The four-particle EPR entangled state | p,χ₂,χ₃,χ₄〉is constructed. The corresponding quantum mechanical operator with respect to the classical transformation p→e^λ₁p, χ₂→ e^λ₂χ₂, χ₃→e^λ₃χ₃, and χ₄→e^λ₄χ₄ in the state |p,χ₂ ,χ₃ ,χ₄〉is investigated, and the four-mode realization of the SU(1,1) Lie algebra as well as the corresponding squeezing operators are presented.     

Uncertainty study of Bd(Bs)→ γν \bar{ν} Decays

B⁰(B_s) → γν\bar{ν} decays are useful to determining the decay constants f_B(f_{B_{s}}) and B(B_s) meson wave function. Using the B meson wave function determined in hadronic B(B_s) decays, we study the uncertainties due to the types of B meson wave functions. We find that the branching ratios are sensitive to the type of wave functions and input parameters, but the energy spectrum is independent. The predicted branching ratios are (0.45-1.04)× 10^-9 and (2.14-3.27)×10^-8 for B⁰ and B_s decay, respectively.     

Anisotropy of Critical Fields in MgB2： Two-Band Ginzburg-Landau Theory for Layered Superconductors

The temperature dependence of the anisotropy parameter of upper critical field γHc2(T)=H_{c2}^||(T)/H_{c2}^{\bot}(T) and London penetration depth γ_λ(T)=λ_{\perp} (T)/λ_{\bot} (T) are calculated using two-band Ginzburg-Landau theory for layered superconductors. It is shown that, with decreasing temperature the anisotropy parameter γ_{H_{c2}}(T) is increased, while theLondon penetration depth anisotropy γλ(T) reveals n opposite behavior.Results of our calculations are in agreement with experimental datafor single crystal MgB₂ nd with other calculations. Results of an analysis of magnetic field H_c1 in a single vortex between superconducting layers are also presented.     

New Approach for Solving Master Equations in Quantum Optics and Quantum Statistics by Virtue of Thermo-Entangled State Representation

By introducing a fictitious mode to be a counterpart mode of the system mode under review we introduce the entangled state representation <η |, which can arrange master equations of density operators ρ(t) in quantum statisticsas state-vector evolution equations due to the elegant properties of <η |. In this way many master equations (respectively describing damping oscillator, laser, phase sensitive, and phase diffusion processes with different initial density operators) can be concisely solved. Specially, for a damping process characteristic of thedecay constant κ we find that the matrix element of ρ (t) at time t in <η| representation is proportional to that of the initial ρ₀ in the decayed entangled state <ηe^-κt| representation, accompanying with a Gaussian damping factor. Thus we have a new insight about the nature of the dissipative process. We also set up the so-called thermo-entangled state representation of density operators, ρ=∫(d²η /π)< η | ρ> D(η), which is different from all the previous known epresentations.     

Contribution of Electromagnetic Field to Atomic Spin

We examine the contribution of electromagnetic field to the atomic spin, by adopting two different, both gauge invariant definitions of the electromagnetic angular momentum: \vec{J}_I ≡ ∫d³ x ε₀ \vec{r} X (\vec{E} X \vec{B}) and \vec{J}_II ≡ ∫d³ x ( ε₀ \vec{E} X \vec{A}^\bot + ε₀ E_i \vec{r} X \vec{\nabla }A^{\bot}_i ). Notably, at the classical level, \vec{J}_II gives an exactly null result while \vec{J}_I gives a finite value. This suggests that \vec{J}_II leads to a simpler and more reasonable picture of the atomic spin, therefore qualifies as a more appropriate definition of the electromagnetic angular momentum. Our observation gives important hint on the delicate issue of gluon contribution to the nucleon spin.     

常温高压下碳酸根离子的拉曼谱峰标定压力初探

在准静水压的条件下,利用碳化硅压腔和显微拉曼光谱原位测量技术,在0～1.7 GPa压力范围测定22 ℃高压下三种不同的H₂O-Na₂CO₃体系(1.5,2.0,2.5 mol·L-1)中CO2-₃的对称伸缩振动ν_{1 066}拉曼谱峰的变化。结果表明,在室温条件下,碳酸根的ν_{1 066}峰的拉曼位移随着压力的增大而线性增加。三种浓度下ν_{1 066}峰的拉曼位移与压力的拟合直线彼此接近,斜率误差小于1%,偏差小于系统误差,因此在实验误差范围内碳酸根浓度对ν_{1 066}峰随压力变化的行为不存在影响。经过数据拟合得到公式：p/MPa=174.13 Δν_{1 066}/cm-1—59.03(Δν_{1 066}=ν_{1 066}-ν_{1 066}0,ν_{1 066}0为体系零压时碳酸根离子ν_{1 066}峰的拉曼位移)。此公式可以用于常温下在含有纯碳酸钠体系中的压力标定。     

翡翠贻贝珍珠层的XRD和FTIR光谱特征

对翡翠贻贝贝壳的珍珠层、棱柱层进行了XRD和FTIR光谱检测,对文石的ν₁,ν₂及ν₄三个内振动模式的频率进行了分析。文石的ν₁和ν₄带在所有的样品中不存在频率位移现象,与洞穴文石的相关谱带的频率一致;ν₂带频率却存在较大差异,珍珠层、棱柱层的ν₂带存在频率位移,初步推测生物合成文石与热效应有关,内部储存有过剩的能量,可作为研究生物矿化机理的实验依据。     

电子助进化学气相沉积金刚石中发射光谱的空间分布

采用蒙特卡罗方法,对以CH₄/H₂为源料气体的电子助进化学气相沉积(EACVD)金刚石中的氢原子(H_α,H_β,H_γ)、碳原子C(2p3s→2p2：λ=165.7 nm)以及CH(A2Δ→X2Π：λ＝420～440 nm)的发射过程进行了模拟,研究了不同CH₄浓度下各发射谱线的空间分布。结果表明,不同CH₄浓度下各发射谱线在反应空间的大部分区域内均随距灯丝距离的增大而增大,而当到达基片表面附近时有所减弱。随着CH₄浓度的增加,H谱线强度减弱,CH与C谱线强度增强。     

A New Lie Algebra and Its Related Liouville Integrable Hierarchies

A new Lie algebra G and its two types of loop algebras \tilde{G₁} and \tilde{G₂} are constructed. Basing on \tilde{G₁} and \tilde{G₂}, two different isospectral problems are designed, furthermore, two Liouville integrable soliton hierarchies are obtained respectively under the framework of zero curvature equation, which is derived from the compatibility of the isospectral problems expressed by Hirota operators. At the same time, we obtain the Hamiltonian structure of the first hierarchy and the bi-Hamiltonian structure of the second one with the help of the quadratic-form identity.     

山东蒙阴金伯利岩中橄榄石的OH红外光谱研究

山东蒙阴金伯利岩中的橄榄石样品的OH红外光谱研究结果表明,在橄榄石的红外光谱图中,3 800～3 000 cm-1范围内共有60多个ν_OH吸收峰。其中3 800～3 710 cm-1范围内的ν_OH吸收峰主要是由空气中的水蒸气所引起的,并非橄榄石的本质或非本质ν_OH;3 710～3 620 cm-1范围内的ν_OH吸收峰主要归属于蛇纹石、滑石、含镁闪石三种含水蚀变矿物相,是橄榄石的非本质ν_OH。含水矿物相中的H主要是在金伯利岩浆后期侵位期间进入橄榄石的;3 620～3 425 cm-1范围内的ν_OH吸收峰源于H占据橄榄石结构中的Si空位后形成的硅镁石型缺陷,及(或)H占据橄榄石结构中的(Mg,Fe)等阳离子空位后形成的缺陷,因而是橄榄石的本质ν_OH。H主要是在地幔环境中,当橄榄石存在于高温的、富流体的金伯利岩浆中时进入橄榄石的;3 425～3 000 cm-1范围内的ν_OH吸收峰主要是由流体水分子所引起的,是橄榄石的非本质ν_OH。流体水可以在地幔环境中,也可以在金伯利岩浆后期侵位期间进入橄榄石。     

Laser-Manipulating Macroscopic Quantum States of a Bose-Einstein Condensate Held in a Kronig-Penny Potential

We investigate the boundary value problem (BVP) of a quasi-one-dimensional Gross-Pitaevskii equation with the Kronig-Penney potential (KPP) of period d, which governs a repulsive Bose-Einstein condensate. Under the zero and periodicboundary conditions, we show how to determine n exact stationary eigenstates {R_n} corresponding to different chemical potentials {μ_n} from the known solutions of the system. The n-th eigenstate R_n is the Jacobian elliptic function with period 2d/n for n=1,2,..., and with zero points containing the potential barrier positions. So R_n is differentiable at any spatial point and R_n² describes n complete wave-packets in each period of the KPP. It is revealed that one can use a laser pulse modeled by a δ potential at site x_i to manipulate the transitions from the states of {R_n} with zero point x≠ x_i to the states of {R_n'} with zero point x= x_i. The results suggest an experimental scheme for applying BEC to test the BVP and to observe the macroscopic quantum transitions.