THE B-S EQUATION OF THE COMPLEX SCALAR FIELD

The renormalization properties of the self-interacting complex scalar field are discussed, its Dyson equation is the presented,the B-S equation of the identical- bosons and relation between the irreducible kernel and the vertex function are derived.     

氦-3熔化压力方程

在广泛收集实验数据和理论关联式的基础上,提出了低温流体3He的宽温区、高精度熔化压力方程。该方程采用国际标准单位制,首次以统一而非分段的形式描述了3He在0．001 K-30 K宽温区熔化压力与温度的关系,方程计算值相对于406个实验数据点的最大和平均偏差分别为3．02％和0．106％。计算表明,该方程在0．31586 K时存在最小压力 2．93113 MPa,这一结论与以往的实验和理论研究非常吻合。     

KdV方程的直接微扰方法

系统地讨论了含修正项的KdV方程的直接微扰方法.从反散射变换所得的不含修正项方程的严格多孤子解出发,导出了线性化算子的零本征值的所有本征函数——平方Jost函数.引入了它们所对应的伴随函数和定义了内积.计算了应有的正交关系,并自然得到单位元的平方Jost函数的展开式.利用广义的Marchenko方程,证明了平方Jost函数的完备性.同时得到展开式中的积分是沿实轴从－∞到∞,但在原点附近将从上方绕过.这不同于过去所得的Cauchy主值积分.为最明确显示这一差别,在单孤子情况下又用平方Jost函数的显式,直接作了验证．同时指出,以前由于取Cauchy主值积分导出的KdV方程所特有的孤子尾,在采用从上方绕过原点的积分时,则事实上并不存在． 关键词：     

高能带电粒子Fokker-PLanck方程的数值解

本文用"空间和能量双向一维差分方法",数值解了带有能量弥散项的高能带电粒子的Fokker Planck方程。在此基础上计算了对背景等离子体的总能量输运,以及转移给电子和离子的能量份额。所得经果与其它方法的计算结果进行了比较。     

自旋玻璃系统的量子输运方程

通过引入电子的弹性散射和非弹性散射的自能和相应的物理格林函数，将磁场中的Ｍａｈａｎ－Ｈ?ｎｓｃｈ量子输运方程推广到自旋玻璃系统中，在电子的近弹性散射近似下，求解了ｓ－ｄ交换相互作用导致的自旋玻璃态霍耳电导；获得了电阻率与自旋玻璃Ｅｄｗａｒｄｓ－Ａｎｄｅｒｓｏｎ（ＥＡ）序参数和局域磁化率之间的关系；讨论了自旋玻璃热电势和特征温度。 关键词：     

湍流等离子体中的重整化色散方程

从速度v的傅里叶空间K的动力学方程出发,采用算子运算及变换方法,可较简便的算出静电湍流场中的重整化色散方程,在以有效关联时间代替湍流场的时、空关联的近似下,计算了有限关联时间效应的作用,表明它是削弱湍流场影响的。短关联时间极限可看成是湍流场影响的上限估计。讨论了湍流场对离声波、电子朗缪波和低频漂移波的影响。 关键词：     

Transmission of light through a random small-angle scattering medium

A theory of random small-angle scattering is presented. The photon dispersion partial differential equation is derived and the dispersion coefficient characterizing the medium is introduced. The equation is solved for a spatial impulse. The modulation transfer function and the contrast loss are derived as a funcion of spatial frequency, dispersion coefficient, and object-to-image distance. The limitation on resolution is shown by an indeterminancy relation based on the dispersion coefficient. The dispersion angle (rms value of scattering angle) is calculated as an example.     

旋转系统内流动分离的渐进结构方程

本文运用量级分析和渐进展开匹配方法推导了适用于旋转系统流动分离的渐进结构方程，此方程具有三层结构的特点，每层有不同的流动性质，层与层之间通过匹配关系联系起来，旋转效应在渐进结构中不出现。由于层间参数的传递反映了该方程及其定解条件的椭圆型特征，加之三层区域的精细结构，该方程为激波／边界层干扰的计算提供了手段。     

Isomorphs in the phase diagram of a model liquid without inverse power law repulsion

Zeroth-order complex dispersion equation of a cylindrical metallic nanowire has been solved analytically to get dispersion relations of surface plasmon-polaritons (SPPs) by approximate methods. The back bending of the dispersion relation can be well described by the analytical solutions, confirming that the back bending is originated from the metal Ohmic loss. Basing on the analytical solutions, the back bending point of the dispersion relation used for the measurement of the metallic Ohmic loss has also been suggested.     

A new approximate analytical approach for dispersion relation of the nonlinear Klein-Gordon equation

A novel approach is presented for obtaining approximate analytical expressions for the dispersion relation of periodic wavetrains in the nonlinear Klein-Gordon equation with even potential function. By coupling linearization of the governing equation with the method of harmonic balance, we establish two general analytical approximate formulas for the dispersion relation, which depends on the amplitude of the periodic wavetrain. These formulas are valid for small as well as large amplitude of the wavetrain. They are also applicable to the large amplitude regime, which the conventional perturbation method fails to provide any solution, of the nonlinear system under study. Three examples are demonstrated to illustrate the excellent approximate solutions of the proposed formulas with respect to the exact solutions of the dispersion relation. (c) 2001 American Institute of Physics.     

MENELAUS RELATION,HIROTA–MIWA EQUATION AND FAY'S TRISECANT FORMULA ARE ASSOCIATIVITY EQUATIONS

It is shown that the celebrated Menelaus relation, Hirota–Miwa bilinear equation for KP hierarchy and Fay's trisecant formula similar to the WDVV equation are associativity conditions for structure constants of certain three-dimensional quasi-algebra.     

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研究了强耦合尘埃等离子体的尘埃声波的线性色散关系和尘埃声孤波的非线性传播。考虑一个包含电子、离子、正电扰动尘埃颗粒的完全电离的三成分模型等离子体。假定其电子、离子数密度服从玻尔兹曼分布,而大质量的尘埃成分用一组经典流体方程描述,对系统方程进行线性化,得到了尘埃声波的线性色散关系,发现离子的集中参数对色散关系的影响很大。用约化摄动法对系统方程进行展开,得到了描述小振幅孤波的伯格斯方程。基于伯格斯方程研究了尘埃声孤波的基本特性,发现尘埃颗粒的强耦合效应对尘埃声孤波有很大的修正作用。该研究结果有助于理解尘埃空间等离子体中局域波的一些特性。     

NLS+方程的平方Jost解的完备性

对于NLS⁺方程相应的平方Jost函数的完备性,通过求得的广义Marchenko方程给出了证明,从而建立了含修正项的直接微扰理论． 关键词：     

强耦合尘埃等离子体中正电扰动下的尘埃声激波

研究了强耦合尘埃等离子体的尘埃声波的线性色散关系和尘埃声孤波的非线性传播。考虑一个包含电子、离子、正电扰动尘埃颗粒的完全电离的三成分模型等离子体。假定其电子、离子数密度服从玻尔兹曼分布,而大质量的尘埃成分用一组经典流体方程描述,对系统方程进行线性化,得到了尘埃声波的线性色散关系,发现离子的集中参数对色散关系的影响很大。用约化摄动法对系统方程进行展开,得到了描述小振幅孤波的伯格斯方程。基于伯格斯方程研究了尘埃声孤波的基本特性,发现尘埃颗粒的强耦合效应对尘埃声孤波有很大的修正作用。该研究结果有助于理解尘埃空间等离子体中局域波的一些特性。     

ON THE HERMITIAN OF THE HAMILTONIAN OF RADIAL EQUATION

The Hamiltonian of a radial equation is defined on a half-line,and there is a close relation between its hermitian and the boundary condition of the wave functions at the origin.If the wave functions are nonvanishing and convergent at the origin,the Hamiltonian has a one-parameter family of self-adjoint extensions which are related with the vanishness of the radial probability current at the origin.In this paper the problem on the hermitian of the Hamiltonian of a radial equation is studied systematically.Some methods for determining the parameter for the fermion moving in the magnetic monopole field are discussed.     

Coaxial configuration of the dielectric Cherenkov maser

The linearized Lorentz force, continuity equation, and Maxwell's equations are used to calculate the system dispersion relation for a coaxial configuration of the dielectric Cherenkov maser. The system consists of two coaxial conductors lined with dielectric and an annular relativistic electron beam, which propagates between the two liners. The dispersion relation for the beam and dielectric-lined coaxial waveguide structure and the no-beam system that describes the dependence of the generated frequency on the coaxial waveguide parameters are presented. Using the linearized dispersion relation, the growth rate for the beam-TM_0n waveguide mode instability is calculated in the strong-coupling tenuous beam limit     

Unveiling the Link Between Fractional Schrödinger Equation and Light Propagation in Honeycomb Lattice

We suggest a real physical system — the honeycomb lattice — as a possible realization of the fractional Schrödinger equation (FSE) system, through utilization of the Dirac‐Weyl equation (DWE). The fractional Laplacian in FSE causes modulation of the dispersion relation of the system, which becomes linear in the limiting case. In the honeycomb lattice, the dispersion relation is already linear around the Dirac point, suggesting a possible connection with the FSE, since both models can be reduced to the one described by the DWE. Thus, we propagate Gaussian beams in three ways: according to FSE, honeycomb lattice around the Dirac point, and DWE, to discover universal behavior — the conical diffraction. However, if an additional potential is brought into the system, the similarity in behavior is broken, because the added potential serves as a perturbation that breaks the translational periodicity of honeycomb lattice and destroys Dirac cones in the dispersion relation.     

单模光纤色散的解析形式

根据波导标量解本征值方程及其递推关系,提出一种利用Gloge关系求解单模光纤中波导色散的理论方法,给出了色散的解析形式,通过分析归一化传输常数的近似解与精确解间的差别论证了这种解析法具有精确求解的计算精度,给出普通单模光纤（G．652）光纤色散的实验数据,并与计算的色散解析解曲线加以比较,二者达到极好的吻合,利用所得到的结果,分析了数值微分法和经验公式的计算精度。     

Fokker-Planck方程的数值解

采用扩散模型研究核裂变,需要求解Fokker-Planck方程。本文提出一个数值计算方法-平均隐式差分方法。对具有粘滞性的核体系的有关裂变动力学量,如几率分布、裂变率、断点处的平均动能以及鞍点到断点的平均扩散时间等一系列物理量做了计算,并与适合大粘滞性的Kramers的解析解做了比较。通过与解析解的比较及对归一常数的检验,证明计算结果精确可靠。     

广义Helmholtz方程的Green函数及旋波介质色散关系的另一求解方法

运用并矢法求解广义Helmholtz方程,结合Fourier变换、留数定理等数学处理,给出方程的并矢Green函数解析表达式;并进一步就旋波介质给出其中色散关系的另外一种求解方法．