作用表示波动方程中与面有关项

这篇短文的内容是:(i)对於量子场论中的i(δψ[σ])/(δσ(x))=V(x,σ)ψ[σ] 如何由寻常的“曲面上的薛定谔方程”导出,作一个较严格的讨论,以及 (ii)讨论上式中的V(x,σ)在什么条件下不包含有σ。我们证明了所需的条件是 (?L^I)/(?φ_μ) (?L^I)/(?φ_ν)=(?²L)/(?φ_μ?φ_ν)F(φ,φ_ρ),式中L,L^I代表总拉格朗日及作用拉格朗日,φ代表场量,φ_μ代表φ/x^μ,F(φ,φ_ρ)代表φ及φ_μ的一个任意函数。     

核心天线CP43、CP47的荧光光谱特性

采用快速扫描成象光谱技术对核心天线CP43和CP47的荧光光谱特性进行研究,获取了它们的积分荧光谱,通过积分荧光谱的组分光谱解析,并结合吸收光谱分析认为CP43和CP47具有这样的Chla的光谱特性,CP43:Chla₆₆₀^662.43、Chla₆₆₉^670.23、Chla₆₈₂^684.02,CP47:Chla₆₆₀^664.91、Chla₆₆₉^671.71、Chla₆₈₀^681.35、(Chla_a^e,a代表吸收峰;e代表发射峰);另外长波长组分694.86nm、702.34nm(CP43)、696.02nm(CP47)可能是由吸收>690nm的Chla分子所产生;CP43与CP47相比还存在有Chla₆₇₅^676.32,但是还没有看到CP43具有675nm吸收谱带的报道.对CP43和CP47的荧光光谱分析,认为CP47中的Chla669nm分子团和Chla680nm分子团间的能量传递比CP43中Chla669nm和Chla682nm分子团的能量传递更为有效;β-Car与Chla分子结合状态在CP47中要比CP43中紧密.     

硼羰基络合物正离子B(CO)3+和B2(CO)4+的红外光解离光谱

利用脉冲激光溅射-超声分子束载带方法制备气相硼羰基络合物正离子. 采用红外光解离光谱研究了B(CO)₃⁺、B(CO)₄⁺ 和B₂(CO)₄⁺的振动光谱. 研究结果表明B(CO)₃⁺具有非常强的B-CO键,无法直接获得其红外光解离光谱. 对B(CO)₄⁺的光解离光谱研究表明该离子是一个B(CO)₃⁺和CO之间弱相互作用络合物. 其中B(CO)₃⁺核具有平面D_3h对称性结构,中心硼具有稳定的8电子组态. B₂(CO)₄⁺具有平面的D_2h对称性结构,其中的B-B键包含一个σ键和半个π键. 自然轨道能量分解分析(EDA-NOCV)表明在B(CO)₃⁺和B₂(CO)₄⁺中的B-CO成键作用中OC→B(σ)要比B→CO(π)反馈作用强.     

Fabry-Perot干涉仪研究光谱线超精细结构的理论分析 Ⅱ——一种Fredholm第一类积分方程稳定数值解之分析

在以前的论文中,我们从计算机模拟实验及相关的光学现象出发提出了Fabry—Perot(以下简称F—P)干涉光谱技术中的积分方程 数值求解的稳定条件。本文将进一步从数学上利用积分方程的本征值理论阐明这些稳定条件产生的原因,从而为F—P干涉光谱技术奠定坚实的基础。     

Ni离子注入多晶ZrO2的表面电性能和结构

对氧化钇(Y₂O₃)部分稳定氧化锆(ZrO₂)样品在室温下进行了Ni离子注入(140kev,5×10¹⁵-2×10¹⁷ios/cm²)和热退火处理.应用电学测量,Rutherford背散射技术(RBS),X射线光电子能谱(XPS)和喇曼光谱方法研究了Ni离子注入多晶ZrO₂的表面电性能,注入层结构及其热退火的影响。     

掺Bi离子锗铌酸盐红外发光玻璃的研究

用高温熔融法制备了Bi₂O₃掺杂的(0.9-x) GeO₂-xNb₂O₅-0.1BaO (含量x为摩尔分数, x=0, 0.04, 0.07, 0.1)系列玻璃. 测定了玻璃样品的差热分析(DTA)曲线、吸收光谱、发射光谱及X射线光电子能谱(XPS). 从DTA曲线分析得到玻璃的结晶起始温度与软化温度之差(T_x-T_g)达200℃以上. 吸收光谱中可观察到位于500, 700, 808和1000 nm处的吸收峰, 并随着Nb₂O₅含量x的增加吸收边带发生红移. 在波长为808 nm激光激发下, 观察到发光中心位于1300 nm处、荧光光谱半高宽约为200 nm的宽带发光. 荧光强度随Bi₂O₃掺杂量δ的增加先增强后减弱, 当掺杂量δ达到约0.01时, 荧光强度达到最强. 随着Nb₂O₅含量x从0.04增加到0.1时, 荧光强度逐步减弱. 样品的XPS峰分别位于159.6和164.7 eV, 它们介于Bi³⁺与Bi⁵⁺的特征结合能之间, 因此Bi³⁺与Bi⁵⁺可能同时存在于玻璃基质中. 从XPS及Bi离子的发光特性推断, 宽带的荧光发射可能起因于Bi⁵⁺. 随着Nb₂O₅含量x的增加, 荧光强度逐步减弱. 分析认为, Nb₂O₅取代GeO₂后形成了NbGe缺陷, 需要低价Bi离子进行电子补偿, 因而抑制了Bi⁵⁺形成, 致使荧光强度减弱.     

关于干涉反演光谱技术能否扩大F-P干涉仪光谱范围的探讨

本文从物理学的角度提出了Fredholm第一类积分方程数值解的可靠性概念,证明了在被称为Fabry-Perot干涉反演光谱技术中,当△σ=2/x,△σ=2/σ时,若取样点数为一个适当的奇数,那么积分方程的数值解是稳定的.但是进一步的计算机模拟实验表明,该数值解不是原积分方程的可靠解,因此,干涉反演光谱技术不能扩大Fabry-Perot干涉仪的光谱范围.理论分析表明,在前述条件下,积分方程数值解不可靠的根本原因在于该积分方程本身没有唯一解.     

Er3+/Yb3+共掺碲钨酸盐玻璃的光谱性质和热稳定性的研究

制备了Er³⁺和Yb³⁺共掺的碲钨酸盐玻璃样品65TeO₂-25 WO₃-10R_mO_n(R_mO_n=PbO,BaO),(65+x)TeO₂-(25-x)WO ₃-10La₂O₃ (x=0,5,10), (60+x)TeO₂-(30 -x)WO₃-10Bi₂O₃ (x=0,5,10).测试了玻璃样品的吸收光谱、荧光光谱、能级寿命及热稳定性能.结果表明除含Bi ₂O₃的碲钨酸盐玻璃外，其余玻璃样品均没出现析晶开始温度(T_x)，说明碲钨酸盐 是一种适合于光纤拉制的玻璃基质材料.应用Judd-Ofelt理论计算了强度参数Ω_t(t=2, 4,6)，研究表明Ω₂在碲钨酸盐玻璃中主要受到Er-O键的共价性的影响，而Er^{3 +} 离子周围配位场的非对称性影响可以忽略.测得了Er³⁺在15 μm发射谱的荧光 半高宽 (FWHM=71—77nm)和Er³⁺的⁴I_13/2能级寿命 (τ^m=3—34 ms).应用McCumber理论计算了Er³⁺在15 μm处的受激发射截面(σ^peak=068—103×10^-20 cm²).比较了Er³⁺在不同玻璃基质里 的15 μm荧光带宽和发射截面，研究结果表明碲钨酸盐玻璃是一种制备宽带光纤放大器的理想基质材料.     

Er3+/Ce3+共掺碲铋酸盐玻璃的制备及光谱特性提高研究

采用高温熔融退火法制备了系列 80TeO₂-10Bi₂O₃-10TiO₂-0.5Er₂O₃-xCe₂O₃ (x=0,0.25, 0.5,0.75,1.0 mol%)和(80-y) TeO₂-10Bi₂O₃-10TiO₂-yWO₃-0.5Er₂O₃-0.75Ce₂O₃ (y=3,6,9,12 mol%)的碲铋酸盐玻璃.测试了玻璃样品400-1700 nm范围内的吸收光谱, 975 nm抽运下的上转换发光谱和1.53 μm波段荧光谱, 以及808 nm激励下的Er³⁺离子荧光寿命和无掺杂玻璃样品的Raman光谱, 并结合Judd-Ofelt理论和McCumber理论计算了Er³⁺离子光谱参数.结果表明, 在掺Er³⁺碲铋酸盐玻璃中引入Ce³⁺离子进行Er³⁺/Ce³⁺共掺, 通过Er³⁺离子⁴I_11/2能级与Ce³⁺离子²F_5/2 能级间基于声子辅助的能量传递过程,可以有效抑制Er³⁺离子上转换发光并明显增强其 1.53 μm波段荧光;同时,在现有Er³⁺/Ce³⁺共掺玻璃组分基础上引入WO₃, 可进一步提高1.53 μm波段荧光并展宽其荧光发射谱. 研究结果对于获取优异光谱特性的宽带掺Er³⁺光纤放大器玻璃基质具有实际意义.     

Ho3+掺杂对ZnO薄膜的微观结构和磁性的影响

研究Ho³⁺掺杂对氧化锌半导体材料的微结构和磁学性质影响. 利用热蒸发技术制备了一系列沉积在Si(100)衬底的Zn_1-xHo_xO(x=0.0、0.04、0.05）薄膜. X射线光谱、表面形貌以及磁性的实验结果表明,Ho³⁺掺杂对ZnO薄膜材料的性能影响很大. X射线衍射图显示峰位出现高角度转变并且趋向于(101)取向,在ZnO晶格显示Ho³⁺置换. 扫描电子显微镜和能谱仪对薄膜的表面形貌以及化学     

Coordinate-dependent 3 + 1 formulation of the general relativity field equations

This paper presents a coordinate-dependent 3+ 1 decomposition of the general relativity field equations in terms of a scalar potentialc ²[(–g ₄₄)^1/2–1], a vector potentialA _icg _4i/(–g₄₄)^1/2, and the three-space metric _ijg _ij–g_4i g _4j/g ₄₄. The equations are exact and the form of the decomposed equations is valid in any coordinate system.     

Relativistic geometrical optics

We investigate the gravitational and electromagnetic fields on the generalized Lagrange space endowed with the metricg _ij(x, y) = _ij(x) + {1 + 1/n ² (x, y)}y _iy_j. The generalized Lagrange spacesM ^m do not reduce to Lagrange spaces. Consequently, they cannot be studied by methods of symplectic geometry. The restriction of the spacesM ^m to a sectionS (M) leads to the Maxwell equations and Einstein equations for the electromagnetic and gravitational fields in dispersive media with the refractive indexn(x, V) endowed with the Synge metric. Whenn(x, V) = 1 we have the classical Einstein equations. If 1/n ²=1–1/c ² (c being the light velocity), we get results given previously by the authors. The present paper is a detailed version of a work in preparation.     

Gravitational field equations based on Finsler geometry

The analysis of a previous paper (see Ref. 1), in which the possibility of a Finslerian generalization of the equations of motion of gravitational field sources was demonstrated, is extended by developing the Finslerian generalization of the gravitational field equations on the basis of the complete contractionK = K _lj ^lj of the Finslerian curvature tensorK _l ^j _hk (x, y). The relevant Lagrangian is constructed by the replacement of the directional variabley ⁱ inK by a vector fieldy ⁱ (x), so that the notion of osculation may be regarded as the key concept on which the approach is based. The introduction of the auxiliary vector fieldy ⁱ (x) is shown to be of physical significance, for the field equations refer not only to the proper field variables but also to a special coordinate system associated withy ⁱ (x) through the Clebsch representation of the latter. The status of the conservation laws proves to be similar to that in the theory of the Yang-Mills field. By choosing a special Finslerian metric function we elucidate in detail the structure of the field equations in the static case.     

Information and gravitation

An information-theoretic approach is shown to derive both the classical weak-field equations and the quantum phenomenon of metric fluctuation within the Planck length. A key result is that the weak-field metric is proportional to a probability amplitude φ_uv, on quantum fluctuations in four-position. Also derived is the correct form for the Planck quantum length, and the prediction that the cosmological constant is zero. The overall approach utilizes the concept of the Fisher information I acquired in a measurement of the weak-field metric. An associated physical information K is defined as K=I−J, where J is the information that is intrinsic to the physics (stress-energy tensor T_μv) of the measurement scenario. A posited conservation of information change δI=ΔJ implies a variational principle δK=0. The solution is the weak-field equations in the metric and associated equations in the probability amplitudes φ_uv. The gauge condition φ _v ^uv =0 (Lorentz condition) and conservation of energy and momentum T_v ^μv=0 are used. A well-known “bootstrapping” argument allows the weak-field assumption to be lifted, resulting in the usual Einstein field equations. A special solution of these is well known to be the geodesic equations of motion of a particle. Thus, the information approach derives the classical field equations and equations of motion, as well as the quantum nature of the probability amplitudes φ_uv.     

Classical electrodynamics with nonlocal constitutive equations

It is assumed that the coupling of the field quantities D^μv (x) and F _αβ (x) is nonlocal. This hypothesis leads to a theory of an electromagnetic field that has the following properties.(1) The source of the field F _αβ (x) exhibits a center of charge and a center of mass that do not coincide, in general.(2) The field componentF _0i=?c²E_i is regular at the origin.(3) In the first-order approximation the new field equations are equivalent to the conventional Maxwell field equations.(4) The conventional cutoff procedure in momentum space as practiced in the Maxwell-Lorentz theory is equivalent to the first-order approximation in terms of an invariant length ξ².(5) The gyromagnetic ratio of the source of F _αβ (x) is equal toc/mc for a quantum of chargee and massm.     

Three- and five-dimensional considerations of the geometry of Einstein's* g-unified field theory

We study the algebraic and differential geometric structures of three- and five-dimensional^* g-unified field theory, with emphasis on the five-dimensional^* g-unified field theory, in which we derive a new set of powerful recurrence relations which hold in a five-dimensional generalized Riemannian manifoldX ₅ , prove a necessary and sufficient condition for the existence and uniqueness of the solution of the system of the Einstein equations in the first two classes, and find a precise tensorial representation of the Einstein connection in terms of^*g .     

Necessary and sufficient conditions for the existence of a Lagrangian in field theory II. Direct analytic representations of tensorial field equations

By using a characterization of the concept of analytic representation and a variational approach to self-adjointness introduced in a preceding paper, we prove a theorem, according to which a necessary and sufficient condition for a class $\text{C}$², regular, tensorial, quasi-linear system of field equations to admit an ordered direct analytic representation in terms of the Lagrange equations in a region R of its variables is that the system is self-adjoint in R. We point out as a first corollary that if the ordering requirement is removed from the definition of analytic representation, then the condition of self-adjointness of the field equations is only sufficient for the existence of a Lagrangian density. We then provide as a second corollary a methodology for the computation of the Lagrangian density for the representation of self-adjoint quasi-linear tensorial field equations. This methodology is also particularized for ordinary semilinear systems of tensorial field equations through a third corollary. The above results are interpreted from the viewpoint of interactions. We first recover, through a fourth corollary, the conventional structure of the total Lagrangian density L_Tot = Σ_{1 a}ⁿL_Free^(a) + L_Int for the semilinear form of the field equations, and then introduce through a fifth corollary a generalized structure of the type L_Tot = Σ_{1 a}ⁿL_{Int, I}^(a)L_Free^(a) + L_Int.II for t representations of the field equations in the quasi-linear form. Therefore, our analysis seems to indicate that a general form of representing interacting fields is characterized by (n+1)-interaction terms in the Lagrangian: n multiplicative terms and one additive term to the Lagrangian for the free fields.     

On the Riemann theta function of a trigonal curve and solutions of the Boussinesq and KP equations

Recently, considerable progress has been made in understanding the nature of the algebro-geometrical superposition principles for the solutions of nonlinear completely integrable evolution equations, and mainly for the equations related to hyperelliptic Riemann surfaces. Here we find such a superposition formula for particular real solutions of the KP and Boussinesq equations related to the nonhyperelliptic curve ⁴ = ( – E ₁) ( – E ₂) ( – E ₃) ( – E ₄). It is shown that the associated Riemann theta function may be decomposed into a sum containing two terms, each term being the product of three one-dimensional theta functions. The space and time variables of the KP and Boussinesq equations enter into the arguments of these one-dimensional theta functions in a linear way.On leave from Leningrad State University and Leningrad Institute of Aviation Instrumentation.     

Unpolarized structure functions and the parton distributions for nucleon in an independent quark model

Considering the nucleon as consisting entirely of its valence quarks confined independently in a scalar-vector harmonic potential; unpolarized structure functions F ₁(x, μ ²) and F ₂(x, μ ²) are derived in the Bjorken limit under certain simplifying assumptions; from which valence quark distribution functions u _v(x, μ ²) and d _v(x, μ ²) are appropriately extracted satisfying the normalization constraints. QCD-evolution of these input distributions from a model scale of μ ²=0.07 GeV² to a higher Q ² scale of Q ₀ ² =15 GeV² yields xu _v(x, Q ₀ ² ) and xd _v(x, Q ₀ ² ) in good agreement with experimental data. The gluon and sea-quark distributions such as G(x, Q ₀ ² ) and q _s(x, Q ₀ ² ) are dynamically generated with a reasonable qualitative agreement with the available data; using the leading order renormalization group equations with appropriate valence-quark distributions as the input.