The ground state properties of the He4-nucleus

Conclusions Table VIII summarizes the computed binding energy of He⁴-nucleus which includes the zeroth order contribution and the correction up to the third order for three different potentials. The binding energy does not contain the C.M. energy, which has been calculated up to the second order. The r.m.s. radii corrected for the C.M. motion and for not-point-like nucleons are calculated up to the second order for potential RHEL 1 and up to the first order for Reid and RHEL 2 potentials. The binding energy and r.m.s. radii are computed for two different self-consistent conditions, the first of which is the usual classical condition (2.16), the second reads E ⁽¹⁾ = 0.In all cases the absolute value of the binding energy of the He⁴-nucleus is lower than the experimental value.It has been shown that the perturbation series built up on the Goldstone reaction matrix diverges, when a self-consistent technique is not used. This represents certain danger also for the self-consistent formulation, although it gives plausible results up to the third order. The result obtained seems to indicate that the discrepancy between the experimental and theoretical values for the binding energy may be caused by neglect of some fundamental facts (relativistic effects, many-body forces etc.) in the present many-body theory.The authors would like to thank the Rutherford High Energy Laboratory for the help in performing necessary computations and for the encouraging interest in this problem.     

Higher order elastic constants of alkali halides

The Coulomb, van der Waals and repulsive lattice sums occurring in the higher order elastic constants up to sixth order have been calculated for the rocksalt and cesium chloride structures. Numerical values of the static elastic constants up to sixth order based on a rigid ion model with van der Waals and Born-Mayer type central force interaction between first and second nearest neighbors are calculated for several alkali halides representing both structure types. Fair agreement with the available experimental third and fourth order elastic constant data is found.     

人眼大视场波前像差特性研究

应用改进的Hartmann-Shack波前传感器人眼像差仪,测量了5只5.2 mm瞳孔的正常眼,向鼻侧和颞侧两个水平方向50°视场角Zernike第二级到第十级的波前像差. 视场角从鼻侧和颞侧两个水平方向从0°增大到50°时,Zernike第三级波前像差的rms值平均增大2倍;Zernike第四级波前像差的rms值平均增大1.8倍;Zernike第五级到第十级波前像差的rms值平均增大1.7~1.3倍.     

On accuracy and performance of high-order finite volume methods in local mean energy model of non-thermal plasmas

In this paper, a high-order finite volume method is employed to solve the local energy approximation model equations for a radio-frequency plasma discharge in a one-dimensional geometry. The so called deferred correction technique, along with high-order Lagrange polynomials, is used to calculate the convection and diffusion fluxes. Temporal discretization is performed using backward difference schemes of first and second orders. Extensive numerical experiments are carried out to evaluate the order and level of accuracy as well as computational efficiency of the various methods implemented in the work. These tests exhibit global convergence rate of up to fourth order for the spatial error, and of up to second order for the temporal error.     

A variational perturbation approximation method in Tsallis non-extensive statistical physics

For the generalized statistical mechanics based on the Tsallis entropy, a variational perturbation approximation method with the principle of minimal sensitivity is developed by calculating the generalized free energy up to the third order in variational perturbation expansion. The approximation up to the first order amounts to a variational approach which covers the variational method developed by E.K. Lenzi, L.C. Malacarne, R.S. Mendes [Phys. Rev. Lett. 80 (1998) 218] and the approximations up to higher orders can systematically improve variational results. As an illustrated example, the generalized free energy for a classical harmonic oscillator (considered in the Lenzi's joint work) are calculated up to the third order, and the resultant approximations up to the first, second, and third orders are numerically compared with the exact result.     

The problem of reggeization in theories with broken global symmetry (II)

The problem of reggeization in renormalizable arbitrarily broken gauge theories is considered. It is shown that the high-energy elastic fermion-fermion amplitude calculated in the leading logarithm approximation up to 8th perturbative order is consistent with an expansion of the amplitude in the Regge-like form (i.e., in which the trajectory is replaced by a matrix function). Similar consistency also holds for the production amplitude calculated up to 5th order. The relations with the reggeization of massive vector mesons are discussed.     

Glueball mass estimate by strong coupling expansion in lattice gauge theories

In the formalism presented in the previous paper, the plaquette-plaquette correlation functions in arbitrary directions are calculated for Z(2), SU(2) and SU(3) up to order g^?8. Approximate restoration of rotational symmetry is observed in the continuum limit for SU(2), but much higher order corrections seem to be required in order to restore the symmetry for SU(3). The scalar glueball mass deduced from the plaquette-plaquette correlation function in the diagonal direction is 0.80 GeV, while the on-axis computation up to order g^?16 predicts it to be 0.64 GeV.     

HIGH TEMPERATURE INTERQUARK POTENTIAL

The high temperature interquark potential within the framework of perturbation theory has been calculated up to the order g⁶. The result is that the quarks are unconfined at high temperature, which is consistent with the Monte Carlo study of the lattice gauge theory. The gluon magnetic mass relevance for the perturbative expansion is analysed. Since the magnetic mass of the gluon is at most of the order g²T, the high-temperatuze interquark potential can be calculates by of perturbation theory only up to the order g¹⁰.     

Numerical solution of differential equations with colored noise

Using the general theory of numerical integration of stochastic differential equations, a constructive approach to numerical methods for a system with colored noise is proposed. Efficient methods up to the 5/2 strong order and up to the third weak order, including Runge-Kutta and implicit schemes, are presented. The algorithms are tested on the Kubo oscillator.     

Higher order QCD effects in inclusive annihilation and deep inelastic scattering

We present a parton model interpretation of the predictions of quantum chromodynamics in the process e⁺e^?→hadron + anything. We give thecomplete list of parameters needed for the study of the scaling violations of fragmentation functions up to the next-to-leading logarithmic approximation. This includes flavour non-singlet and flavour singlet anomalous dimensions up to order α² and coefficient functions up to order α. We also present results for the deep inelastic scattering e^?h→e^? + anything. We find that in e⁺e^? annihilation the ratio of scaling violations of second order to first order is in general bigger than the corresponding ratio for deep inelastic scattering. The Gribov-Lipatov relation is thus violated in second order. We also find that a modified Drell-Yan analytic continuation relation holds between the deep inelastic and annihilation structure functions for quarks and gluons. In x space we give detailed numerical evaluation of the QCD effects for non-singlet and singlet densities, in the space-like and time-like regions.     

Non-perturbational calculation of the Bloch-Siegert effect in semiclassical and quantum approaches

It is reported that it is possible in practice to calculate with a computer the analytical expression of the density matrix elements of a two-level quantum system interacting with an EMF, without using perturbation methods. Formulae including terms up to second order in the coupling are given in the semi-classical case (with and without averaging over the phase of the field) and in the quantum case. Results are in accordance with those of Pegg for the case of the classical EMF averaged over ? Disaccordances with other works are reported and reasons for performing the same calculation up to fourth order are given.     

Magnetic field and pressure dependence of small angle neutron scattering in MnSi

We report small angle neutron scattering of spontaneous and magnetic field aligned components of the helical spin polarization in MnSi for temperatures T down to 0.35 K, at pressures p up to 21 kbar, and magnetic field B up to 0.7 T. The parameter range of our study spans the first order transition between helical order and partial magnetic order at p{c}=14.6 kbar, which coincides with the onset of an extended regime of non-Fermi liquid resistivity. Our study suggests that MnSi above p{c} is not dominated by the remnants of the first order transition at p{c}, but that an unidentified mechanism favors stabilization of a new ground state other than helical order.     

静电四极透镜中非线性传输的Lie代数分析

用Lie代数方法分析了带电粒子在静电四极透镜中的非线性传输,结果为三级近似.分析过程为:首先建立粒子在静电四极透镜中的运动的Hamilton函数,然后将Hamilton函数在平衡轨道附近展开成幂级数,最后计算粒子的非线性轨迹到三级近似.根据需要,还可以扩展到更高级近似解.     

Nonlinear Coherent States and Ehrenfest Time for Schrödinger Equation

We consider the propagation of wave packets for the nonlinear Schrödinger equation, in the semi-classical limit. We establish the existence of a critical size for the initial data, in terms of the Planck constant: if the initial data are too small, the nonlinearity is negligible up to the Ehrenfest time. If the initial data have the critical size, then at leading order the wave function propagates like a coherent state whose envelope is given by a nonlinear equation, up to a time of the same order as the Ehrenfest time. We also prove a nonlinear superposition principle for these nonlinear wave packets.     

电磁交叉场分析器中非线性传输的Lie代数分析

用李代数方法分分析了带电粒子在电磁交叉场分析器中的非线性传输,结果近似到三级近似.分析过程为:首先建立粒子在电磁交叉场分析器中的运动的Hamilton函数,然后将Hamilton函数在平衡轨道附近展开成幂级数,最后计算粒子的非线性轨迹到三级近似.根据需要,还可以推导出更高级的近似解.     

Asymptotic Theory for the Time-Dependent Behavior of a Slightly Rarefied Gas Over a Smooth Solid Boundary

A time-evolution of a slightly rarefied monoatomic gas, namely a gas for small Knudsen numbers, which is perturbed slowly and slightly from a reference uniform equilibrium state at rest is investigated on the basis of the linearized Boltzmann equation. By a systematic asymptotic analysis, a set of fluid-dynamic-type equations and its boundary conditions that describe the gas behavior up to the second order of the Knudsen number are derived. The developed theory covers a general intermolecular potential and a gas-surface interaction. It is shown that (i) the compressibility of the gas manifests itself from the leading order in the energy equation and from the first order in the continuity equation; (ii) although the momentum equation is the Stokes equation, it contains a double Laplacian of the leading order flow velocity as a source term at the second order; (iii) a double Laplacian source term also appears in the energy equation at the second order; (iv) the slip and jump conditions are the same as those in the time-independent case up to the first order, and the difference occurs at the second order in the jump conditions as the terms of the divergence of flow velocity and of the Laplacian of temperature. Numerical values of all the slip and jump coefficients are obtained for a hard-sphere gas by the use of a symmetric relation developed recently.     

Application of the matrizant method to calculate the third-order aberration coefficients for a sector magnetic field including fringing-field effects

The matrizant method is used to study the nonlinear dynamics of charged particles in magnetic sector analyzers. The calculations of matrizants (transfer matrices) allow for both fringing-field effects due to the stray field and higher harmonics of the sector magnetic field (up to the third order). For the rectangular distribution of the field components along the optical axis, analytical expressions for the aberration coefficients (including dispersion ones) are derived up to the third order. In the simulation of real fields with a nonzero stray-field width, the smooth distribution of the field components is employed. The aberration coefficients for this distribution were calculated by means of a conservative numerical method.     

On the third- and fourth-order constants of incompressible isotropic elasticity

Consider the constitutive law for an isotropic elastic solid with the strain-energy function expanded up to the fourth order in the strain and the stress up to the third order in the strain. The stress-strain relation can then be inverted to give the strain in terms of the stress with a view to considering the incompressible limit. For this purpose, use of the logarithmic strain tensor is of particular value. It enables the limiting values of all nine fourth-order elastic constants in the incompressible limit to be evaluated precisely and rigorously. In particular, it is explained why the three constants of fourth-order incompressible elasticity μ, ā, and D are of the same order of magnitude. Several examples of application of the results follow, including determination of the acoustoelastic coefficients in incompressible solids and the limiting values of the coefficients of nonlinearity for elastic wave propagation.     

Interpolating Hamiltonians for a stochastic-web map with quasicrystalline symmetry

A systematic Hamiltonian approximation scheme is developed for a stochastic-web map with fivefold quasicrystalline symmetry. Interpolating Hamiltonians are calculated up to tenth order in the control parameter a. The higher order Hamiltonians are used to provide bounds for closed invariant curves of the map, and to investigate the structural evolution of map's phase portrait for a相似文献   

Energy-momentum dispersion of glueballs and the restoration of Lorentz invariance in lattice gauge theories

The strong-coupling expansion for the energy-momentum dispersion of the scalar glueball is carried out for euclidean Z₂ and SU(2) lattice gauge theories up to 10th order in 3 dimensions and to 8th order in 4 dimensions. The results are used to study the restoration of Lorentz invariance in the continuum limit.