恒流电场和恒流电路方程

恒流电场和恒流电路方程①左卫群（桂林电子工业学院桂林５４１００４）１恒流电场方程电流场一个重要的基本性质是它的连续方程，即（Ｓ）ｊｄｓ＝－ｄｑｄｔ表明在单位时间内，从任意一个闭合曲面Ｓ内流出的电量（Ｓ）ｊｄｓ等于单位时间Ｓ面内电荷的减少量－ｄ...     

二体和三体核反应对称性运动学方程

利用对称性分析了二体和三体核反应运动方程,得出：（1）二体核反应运动方程在转动不变群下实质是单值;（2）三体核反应运动方程在两个转动不变群下实际变元只有一个,在这个变元一定的情况下,通过两个转动不变群得到的三体核反应运动方程的解实质上是等价的。     

二十面体群拉曼和超拉曼张量的计算

本文简单介绍了计算张量的不变式－协变式方法，以及根据此原理所编程序的设计思想，并在附录中给出了二十面体群（Ⅰ群）的Ｒａｍａｎ、Ｈｙｐｅｒ Ｒａｍａｎ对称（α、β、γ）张量和非对称（α－、β－、γ－）［１］张量。     

含时空关联噪声生长方程的标度奇异性分析

基于动力学重整化群理论研究表面界面生长动力学标度奇异性问题, 得到含时空关联噪声的表面生长方程标度奇异指数的一般结果,并将此方法应用于几种典型的局域生长方程——Kardar-Parisi-Zhang（KPZ）方程、线性生长方程、Lai-Das Sarma-Villain（LDV）方程.结果表明,在长波长极限下局域生长方程的动力学标度奇异性与最相关项、基底维数以及噪声有关,并且若出现标度奇异性,只会是超粗化（super rough）奇异标度行为,而不是内禀（intrinsically）奇异标度行为. 关键词： 标度奇异性 动力学重整化群理论 时空关联噪声     

耦合SU(5) EYMH系统的静态双荷黑洞

研究耦合ＳＵ（５）Ｅｉｎｓｔｅｉｎ－Ｙａｎｇ－Ｍｉｌｌｓ－Ｈｉｇｇｓ（ＥＹＭＨ）系统。得到了场方程的一类静态球对称Ｒｅｉｓｓｎｅｒ－Ｎｏｒｄｓｔｒｏｍ（Ｒ－Ｎ）型解，它代表具有ＳＵ（５）双荷子（磁荷为±3/(2e)）的静态黑洞。 关键词：     

H~-的激发态

长期以来,人们一般认为Ｈ－只有一个束缚基态而没有其他束簿态,本文利用解体法（将Ｈ－的两体方程分解成两个单体方程）证明Ｈ－存在着无限多个激发态,在形成束缚态的过程中简并起了重要作用．     

临界点附近的H2气体的状态方程

将Ｂｅｎｅｄｉｃｔ－Ｗｅｂｂ－Ｒｕｂｉｎ（ＢＷＲ）方程应用于Ｈ２气体,采用非线性最小二乘法,精选参与拟合的实验数据和初始参数,拟合出了适用于温度３０Ｋ－７００Ｋ、压强０．１ａｔｍ－１００．００ａｔｍ范围Ｈ２气体的有关参数,进而作了全部Ｐ－Ｖ－Ｔ回代计算,通过计算值与实验值的比较发现：Ｈ２气体温度在临界点附近（３０Ｋ－４０Ｋ）,压强达１００．００ａｔｍ和密度超过临界密度ρｃ的两倍时,ＢＷＲ方程仍能计     

PuⅠ偶宇称光谱能级的模式识别研究

本文利用偏最小二乘法（ＰＬＳ）－反向传播网络（ＢＰＮ）方程对ＰｕⅠ偶宇称光谱有级进行了指认,结果与实验相符。表明ＰＬＳ－ＢＰＮ可用于复杂子光谱能级归属的分类。     

用多重网格TVD－LW格式数值求解N－S方程

用多重网格ＴＶＤ－ＬＷ格式数值求解Ｎ－Ｓ方程刘建军，蒋洪德（中国科学院工程热物理研究所北京１０００８０）关键词：ＴＶＤ－ＬＷ格式，Ｎ－Ｓ方程一、前言用时间推进法数值求解雷诺平均Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程，不仅能够模拟从低亚音速到高超音速的复杂定常...     

类氦离子1,3P激发态Schrodinger方程的直接解

利用相关函数（ＣＦ）－超球谐（ＨＨ）－广义Ｌａｇｕｅｒｒｅ（ＧＬＦ）方法直接求解类氦离子ｎ＾１,３Ｐ（ｎ＝１,２,３）低躺激发态的Ｓｃｈｒ¨／ｏｄｉｎｇｅｒ方程,得氦原子的本征能量分别为－２．１３３１７Ｅｈ（１＾３Ｐ）,－２．１２３８３Ｅｈ（１＾１Ｐ）,－２．０５８１０Ｅｈ（２＾３Ｐ）,－２．０５５１６Ｅｈ（２＾１Ｐ）,－２．０３２３５Ｅｈ（３＾３Ｐ）和－２．０３１０９Ｅｈ（３＾１Ｐ）,它们与文献     

原子-辐射场相互作用系统 Heisenberg运动方程的相干态表述

用Heisenberg-Weyle(简称H-W)群直积SU(2)群上的相干态表述了原 子-辐射场相互作用系统的Heisenberg运动方程。引入一个算符振幅函数,将Heisenberg绘 景中算符运动方程转化成可分离变量的偏微分方程,给出了方程的形式解以及时间演化算符 在该表述下的表示。     

处理原子-辐射场相互作用系统的变分方法

用Heisenberg-Weyl(简H-W)群直积SU(2)群上的相干态表述了原子-辐射场相互作用系统的非平衡态统计力学.引入一个新定义的含时分布函数,将非平衡态下密度矩阵所满足的von Neumann方程转化成可分离变量的偏微分方程,给出了方程的形式解,算符的平均值表示.本文还就便于作微扰展开的相互作用绘景作了讨论.     

Stationary momentum space solution of the Fokker-Planck equation for a simple model of a laser oscillator exhibiting spatial dispersion

Starting from a multimode hamiltonian for a system of radiating oscillators coupled with atomic reservoirs, the secular master equation for the radiation-density operator is calculated in the interaction picture after elimination of the atomic variables. Using the differential operator representation for coherent states this equation is transcribed into a multimode Fokker-Planck equation. The stationary solution in momentum space is given for the threshold region. Fourier transformation to configuration space results in a quasi-free energy formula for a laser oscillator exhibiting spatial dispersion.     

A Bargmann representation solution of the Jaynes—Cummings model

The dynamics of the Jaynes—Cummings model is solved completely in a Bargmann representation. The result is the power series obtained earlier in the occupation number representation; a suggestive reformulation of the problem in terms of a simple partial differential equation ensues.     

New method of applying conformal group to quantum fields

Most of previous work on applying the conformal group to quantum fields has emphasized its invariant aspects, whereas in this paper we find that the conformal group can give us running quantum fields, with some constants, vertex and Green functions running, compatible with the scaling properties of renormalization group method(RGM). We start with the renormalization group equation(RGE), in which the differential operator happens to be a generator of the conformal group, named dilatation operator. In addition we link the operator/spatial representation and unitary/spinor representation of the conformal group by inquiring a conformal-invariant interaction vertex mimicking the similar process of Lorentz transformation applied to Dirac equation. By this kind of application,we find out that quite a few interaction vertices are separately invariant under certain transformations(generators) of the conformal group. The significance of these transformations and vertices is explained. Using a particular generator of the conformal group, we suggest a new equation analogous to RGE which may lead a system to evolve from asymptotic regime to nonperturbative regime, in contrast to the effect of the conventional RGE from nonperturbative regime to asymptotic regime.     

The Chern-Simons theory and knot polynomials

The Chern-Simons gauge theory is studied using a functional integral quantization. This leads to a differential equation for expectations of Wilson lines. The solution of this differential equation is shown to be simply related to the two-variable Jones polynomial of the corresponding link, in the case where the gauge group isSU(N). A similar equation has been used before to get the Jones polynomial from a braid representation of the link. The main novelty of our approach is that we get the Jones polynomial from a plat representation of the link.     

Propagation of soliton waves in nonlinear dielectric slab waveguides of parabolic index of refraction

The pulse propagation in a non-linear slab waveguide of parabolic index of refraction is treated by using differential equation techniques. A graded index dielectric slab waveguide free of material dispersion with a cubic order non-linearity is considered. The electromagnetic wave inside the waveguide is described in terms of a non-linear equation. Slowly varying envelope function representation is employed to develop a non-linear partial differential equation for the unknown envelope function of the electric field. An averaging method over the transverse direction is applied to reduce the unknown envelope function non-linear differential equation into a form resembling the well known non-linear Schrödinger differential equation. This equation is solved by applying the Inverse Scattering Method. The N-soliton solution is developed and presented explicitly for the practical case of the single mode dielectric slab waveguide. Numerical results presenting single and double soliton propagation are also given.     

Fundamental Solution of the Volkov Problem (Characteristic Representation)

Abstract

The characteristic representation, or Goursat problem, for the Klein-Fock-Gordon equation with Volkov interaction [1] is regarded. It is shown that in this representation the explicit form of the Volkov propagator can be obtained. Using the characteristic representation technique, the Schwinger integral [2] in the Volkov problem can be calculated.     

Spontaneous emission of the non-Wiener type

The spontaneous emission of a quantum particle and superradiation of an ensemble of identical quantum particles in a vacuum electromagnetic field with zero photon density are examined under the conditions of significant Stark particle and field interaction. New fundamental effects are established: suppression of spontaneous emission by the Stark interaction, an additional “decay” shift in energy of the decaying level as a consequence of Stark interaction unrelated to the Lamb and Stark level shifts, excitation conservation phenomena in a sufficiently dense ensemble of identical particles and suppression of superradiaton in the decay of an ensemble of excited quantum particles of a certain density. The main equations describing the emission processes under conditions of significant Stark interaction are obtained in the effective Hamiltonian representation of quantum stochastic differential equations. It is proved that the Stark interaction between a single quantum particle and a broadband electromagnetic field is represented as a quantum Poisson process and the stochastic differential equations are of the non-Wiener (generalized Langevin) type. From the examined case of spontaneous emission of a quantum particle, the main rules are formulated for studying open systems in the effective Hamiltonian representation.     

Reparameterization for statistical state estimation applied to differential equations

The ensemble Kalman filter is a widely applied data assimilation technique useful for improving the forecast of computational models. The main computational cost of the ensemble Kalman filter comes from the numerical integration of each ensemble member forward in time. When the computational model involves a partial differential equation, the degrees of freedom of the solution in the discretization of the spatial domain are oftentimes used for the representation of the state of the system, and the filter is applied to this state vector. We propose a method of approximating the state of a partial differential equation in a representation space developed separately from the numerical method. This representation space represents a reparameterization of the state vector and can be chosen to retain desirable physical features of the solutions. We apply the ensemble Kalman filter to this representation of the state, and numerically demonstrate that acceptable results are obtained with substantially smaller ensemble sizes.