UA(1) anomaly and $ \eta^{{\prime}}_{}$ -mass from an infrared singular quark-gluon vertex

The U _A(1) problem of QCD is inevitably tied to the infrared behaviour of quarks and gluons with its most visible effect being the -mass. A dimensional argument of Kogut and Susskind showed that the mixing of the pseudoscalar flavour-singlet mesons with gluons can provide a screening of the Goldstone pole in this channel if the full quark-quark interaction is strongly infrared singular as ∼ 1/k ⁴ . We investigate this idea using previously obtained results for the Landau gauge ghost and gluon propagator, together with recent determinations for the singular behaviour of the quark-gluon vertex. We find that, even with an infrared vanishing gluon propagator, the singular structure of the quark-gluon vertex for certain kinematics is apposite for yielding a non-zero screening mass.     

Two-vibron bound states in the β--Fermi--Pasta--Ulam model

This paper studies the two-vibron bound states in the β- Fermi Pasta-Ulam model by means of the number conserving approximation combined with the number state method. The results indicate that on-site, adjacent-site and mixed two-vibron bound states may exist in the model. Specially, wave number has a significant effect on such bound states, which may be considered as the quantum effects of the localized states in quantum systems.     

Enhanced spontaneous emission factor for microcavity lasers

The microcavity and the influence of nonradiative recombination can control spontaneous emission. An analytic resolution of rate equation is studied for microcavity lasers. The relationship between output prop- erties and structural parameters of multi-quantum wells (MQWs) is obtained. One of the most important consequences of the incrcased spontaneous emission factor is the reduction of laser threshold. It is found that the characteristic curve of a "thresholdless" laser is strongly nonradiative depopulation-dependent. The light output is increased by the enhanced well number and the reduced width. In particular, there is an optimal well number corresponding to the lowest threshold current density for MQW structure in the microcavity lasers.     

二维棋盘格子复式晶格的完全光子带隙研究

设计了一种棋盘格子复式晶格的二维光子晶体：在二维正方形格子中，把截面为正方形的柱子旋转45°，同时在每个原胞中心引入一个圆形截面的柱子构成的光子晶体结构. 用平面波展开计算棋盘格子复式晶格的完全光子带隙，结果表明：棋盘格子复式晶格的完全光子带隙的Δω/ω比值几乎是普通棋盘格子的5倍，完全光子带隙的个数也增加. 与其他复式结构相比较，发现其最佳的Δω/ω比值是一类粗锐复合结构光子晶体的2.1倍. 关键词： 二维光子晶体 复式晶格 完全光子带隙     

Two-dimensional commensurate soliton structures

A phase diagram of pinned soliton structures in two dimensions has been found for a repulsive interactionU(x) between solitons withU(x)>0. The critical fugacity of the commensurate soliton structure is shown to be proportional toU(l), wherel is the period of this structure.     

Fractal behavior in trapping and reaction: A random walk study

We investigate the trapping of a random walker in fractal structures (Sierpinski gaskets) with randomly distributed traps. The survival probability is determined from the number of distinct sites visited in the trap-free fractals. We show that the short-time behavior and the long-time tails of the survival probability are governed by the spectral dimensiond. We interpolate between these two limits by introducing a scaling law. An extension of the theory, which includes a continuous-time random walk on fractals, is discussed as well as the case of direct trapping. The latter case is shown to be governed by the fractal dimensiond.     

Scaling properties of ℤ k- 1 actions on the circle

We derive universal scaling properties for ^k–1 actions on the circle whose generators have rotation numbers algebraic of degreek. As fork=2 these properties can be explained for arbitraryk in terms of a renormalization group transformation. It has at least one trivial fixed point corresponding to an action whose generators are pure rotations. The spectrum of the linearized transformation in this fixed point is analyzed completely. The fixed point is hyperbolic with a (k–1)-dimensional unstable manifold. In the casek=2 the known results are therefore recovered.     

A bound on the number of bound states in the Schrödinger equation

A boundS _l is given for the number of bound statesn _i in thelth partial wave corresponding to a spherically symmetric potential in non-relativistic quantum mechanics. This bound is given by whereV _a(l, r) is the attractive part of the effective potentialV(r)+l(l+1)/r ². Extensive comparative study ofS _i and the Bargmann inequality is made.     

双图的一些脆弱性参数

一个图G的双图（double graphs）的定义为D[G]=G×T2,这里×表示图的直积,而死表示两个顶点的全图．本文研究了图的双图的一些脆弱性参数．     

Numerical solution of a viscous incompressible flow problem through an orifice

A steady flow problem of a viscous, incompressible fluid through an orifice is widely applicable to many physical phenomena and has been studied previously by many researchers. A problem of such type has been solved by applying LAD method given by Roache [1]. The resulting system of linear equations is solved by Hockney's method [2].