Solutions of the Fokker-Planck equation for a double-well potential in terms of matrix continued fractions

Solutions of the Fokker-Planck (Kramers) equation in position-velocity space for the double-well potentiald ₂x²/2+d₄x⁴/4 in terms of matrix continued fractions are derived. It is shown that the method is also applicable to a Boltzmann equation with a BGK collision operator. Results of eigenvalues and of the Fourier transform of correlation functions are presented explicitly. The lowest nonzero eigenvalue is compared with the escape rate in the weak noise limit for various damping constants and the susceptibility is compared with the zero-friction-limit result.     

Some neutral current effects in an SU(3)×U(1) gauge model

The anomalous magnetic moment of muon is calculated in anSU(3)×U(1) gauge model proposed by Gupta and Mani. We find the contribution due to the intermediate gauge bosons to be of the same order of magnitude as in Weinberg. Salam model. The deep-inelastic structure functions are also analysed in the same model and inequalities for the structure functions are obtained in the light-cone algebra approach.     

An exactly soluble case of the triangular ising model in a magnetic field

An anisotropic triangular Ising model in which the first- and second-order parameters and the field parameters are functionally related is solved exactly by representing the distribution of the atom patterns in terms of a suitably constructed Markov process. The probabilities of patterns, defined as the probabilities generated by this process, are a mathematically tractable alternative to the classical representation of these probabilities in terms of the partition function. The interaction and field parameters of this Ising model, its magnetization, free energy, and its nearest neighbor correlation functions, are expressed in terms of the parameters of this Markov process. Special cases are worked out in detail and numerical examples are given.     

Debye screening for two-dimensional Coulomb systems at high temperatures

The grand canonical ensemble of a two-dimensional Coulomb system with±1 charges is proved to have screening phenomena in its high-temperature region. The Coulomb potential in a finite region is assumed to be (–)^–1, where is the Laplacian with zero boundary conditions on. The hard-core condition is not assumed. The model is set up by separating (–)^–1 into a shortrange part and a long-range part depending on a parameter. The self-energies are subtracted only for the short-range part and therefore a choice of is a choice of subtraction of self-energies. The method of proof is in general the same as that of Brydges-Federbush Debye screening, except that here a modification for the short-range part of the potentials is needed.     

On the metric properties of the Feigenbaum attractor

The two standard literature definitions of the function associated with the Feigenbaum attractor are not equivalent. The method due to Vulet al. and Feigenbaum is used to calculate the Haussdorff dimension of the Feigenbaum attractor, using as input the trajectory scaling functions. The two calculations yield the same Hausdorff dimensionD=0.5380451435 to within the accuracy of the computation.     

关于Hale问题

本文推广了林振声关于 Hale 问题的解答,利用微分系统的指数型三分性给出了弱概周期微分系统中心积分流形的存在性定理.     

Analysis of two neutron (proton) transfer reaction data in the Zr-region

The spectroscopic amplitudes, form factors, angular distributions and total cross-sections for two nucleon transfer reactions in Zr-region in the zero range distorted wave Born approximation are calculated using consistent set of shell model wave functions. A single normalisation factor gives a good fit to all the two neutron transfer reaction data whereas the corresponding fit for the two-proton transfer reaction data is less satisfactory.     

Exact expressions for row correlation functions in the isotropicd=2 ising model

We present exact explicit expressions for the row spin-spin correlation functions _{00 n}0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for _{00 n}0.     

一种新的奇偶非线性相干态的位相统计性质

根据Pegg-Barnett位相定义, 计算了一种新的奇偶非线性相干态的位相概率分布函数, 利用数值计算方法研究了它们的位相统计性质. 数值计算结果表明：新的奇偶非线性相干态的位相特性与通常奇偶相干态的位相特性截然不同.