Letter: Solar Gravitational Deflection of a Graviton

The solar gravitational deflection angle of a graviton is calculated through the scattering cross section of the graviton by the sun and shown to be equal to the light deflection angle as calculated from the null geodesic equation of general relativity.     

Forces along Equidistant Particle Paths

Two particles on the sphere leave the equator moving due south and travel at a constant and equal speed along a geodesic colliding at the south pole. An observer who is unaware of the curvature of the space will conclude that there is an attractive force acting between the particles. On the other hand, if particles travel at the same speed (initially parallel) along geodesics in the hyperbolic plane, then the particle paths diverge. Imagine two particles in the hyperbolic plane that are bound together at a constant distance with their center of mass traveling along a geodesic path at a constant velocity, then the force due to the curvature of the space acts to break the bond and increases as a quadratic function of the velocity. We consider this problem for the sphere and the hyperbolic plane and we give the exact formula for the apparent force between the particles. This revised version was published online in July 2006 with corrections to the Cover Date.     

Smart Geodesic Tracing in GRworkbench

We have developed a new tool for numerical work in General Relativity: GRworkbench. We discuss how GRworkbench's implementation of a numerically-amenable analogue to Differential Geometry facilitates the development of robust and chart-independent numerical algorithms. We consider, as an example, geodesic tracing on two charts covering the exterior Schwarzschild space-time.     

Null Geodesics in Brane World Scenarios

We study the null bulk geodesic motion in the brane world in which the bulk metric has an un-stabilized extra spatial dimension. We find that the null bulk geodesic motion as observed on the 3-brane with Z₂ symmetry would be a timelike geodesic motion even though there exists an extra non-gravitational force in contrast with the case of the stabilized extra spatial dimension. In other words the presence of the extra non-gravitational force would not violate the Z₂ symmetry.     

新面型短程透镜的制备研究

根据解析理论新的精确公式进行设计并用单点金刚石超精切削加工制备,研制出一种优化的非球凹面短程透镜.透镜含光滑无奇点圆边,与平面连接的边缘曲率半径为无限大.样品制备在45×20×2.5mm3的LiNbO3衬底上,每片有两个孔径8mm、焦距8mm的无球差非球面短程透镜,利用670nm波长的半导体激光器端面耦合入样品一端,在另一端测得焦点光斑半宽度为2.9μm.     

波导短程透镜的实验研究

波导透镜是集成光路〔IO〕中的最基本元件,它在IO中的作用类似体光学光路中的透镜.IO光信号处理系统如集成光学声光频谱分析器、导波声光卷积器、相关器、调频脉冲压缩器和矩阵乘法器等.系统中都需要用波导透镜.波导短程透镜较其它形式的波导透镜具有孔径大、旋转对称、无色差和插入损耗小的特点,所以特别引人注意.     

ON GEODESIC COMPLETENESS OF NONDEGENERATE SUBMANIFOLDS IN SEMI-EUCLIDEAN SPACES

In this paper, we study the geodesic completeness of nondegenerate submanifolds in semi-Euclidean spaces by extending the study of Beem and Ehrlich [1] to semi-Euclidean spaces. From the physical point of view, this extend may have a significance that a semi-Euclidean space contains more variety of Lorentzian submanifolds rather than those of Lorentzian hypersurfaces in a Minkowski space as in [1]. From mathematical point of view, since there is no distinction in the analysis of geodesic completeness of Lorentzian submanifolds and nondegenerate submanifolds in a semi-Euclidean space, we treat the mathematically more general case of nondegenerate submanifolds in a semi-Euclidean space. The new ideas leading to this generalization are the sufficient conditions for algorithms in the proofs of the results in [1]. Indeed these sufficient conditions for the algorithms also work well for the nondegenerate submanifolds in a semi-Euclidean space.     

尘埃粒子的时空结构及其性质

讨论了尘埃粒子解的时空结构及其性质，导出了尘埃粒子的内空间的离散结构.证明了尘埃粒子内部的物质球是一个无坐标的平直球，因而具有最小的体积和整体的关联性.导出了在尘埃粒子的内外时空中的径向测地线并说明其连续性.阐述了由这个解所揭示的物质、引力与时空之间的内在联系. 关键词： 尘埃粒子 离散时空 测地线     

Properties of spacetimes with magnetic dipoles

The properties of an asymptotically flat spacetime with a mass and a magnetic dipole are studied. We focus on the breaking of spherical symmetry by the magnetic dipole. We investigate the geometry of the spacetime through the trajectories of null geodesics and the embedding diagrams of various hypersurfaces, included constant t and r surfaces and the infinite red shift surface. We find that the effects of the magnetic dipole on the spacetime are larger at the poles than on the equator.     

Geodesic Incompleteness in the ℂP 1 Model on a Compact Riemann Surface

It is proved that the moduli space of static solutions of the P ¹ model on spacetime ×, where is any compact Riemann surface, is geodesically incomplete with respect to the metric induced by the kinetic energy functional. The geodesic approximation predicts, therefore, that lumps can collapse and form singularities in finite time in these models.     

Generalized Killing Tensors

Generalized Killing tensors are defined and the integrability conditions discussed to show that the familiar result that a space of constant curvature admits the maximum number of Killing vectors and second order Killing tensors does not necessarily generalize. The existence of second order Generalized Killing Yano tensors in spherically symmetric static space-times is investigated and a non-redundant example is given. It is proved that the natural vector analogue of the Lenz-Runge vector does not exist.     

2+1维de-Sitter时空中光线的轨迹

通过求解2+1维de-Sitter时空中零测地线方程得到光线的轨迹方程,对轨迹方程进行分析发现其不存在封闭的轨迹解.     

一类类光测地线的加速度

类光测地线γ0(λ)与二维类空超曲面φ正交，λ为其仿射参量.假如在类光测地线γ0(λ)上存在一点r(r=γ0(λr))共轭于类空超曲面φ，则对于γ0(λ)上任一点q(q=γ0(λq))满足λq＞λr，一定能把γ0连续变形成一条从φ到q的类时曲线.当产生类时曲线的变分矢量场不是类光测地线上的广义Jacobi场时，这些类时曲线在趋于类光测地线时，它们的固有加速度趋于无穷大. 关键词： 类光测地线 共轭点 变分     

A focal index theorem for null geodesics

Employing techniques recently developed by D. Kalish for Riemannian manifolds, we obtain a focal Morse index theorem for a null geodesic segment initially and terminally perpendicular to spacelike submanifolds of arbitrary codimension in a general space-time.     

Central extensions of semidirect products and geodesic equations

We express the equation for stratified fluid and the superconductivity equation as geodesic equations on Lie group central extensions of semidirect products. We study the existence of stream functions.     

Timelike and null geodesics in the Nordström field

The timelike and null geodesics are investigated in the Nordström geometry and it is found that incoming geodesics always encounter a turning point at a finite radial distance. The limits for escape, bound and stable orbits are obtained and they are closer to the source as compared to their counterparts in the Schwarzschild’s field.     

Exponential mixing for the geodesic flow on hyperbolic three-manifolds

We give a short and direct proof of exponential mixing of geodesic flows on compact hyperbolic three-manifolds with respect to the Liouville measure. This complements earlier results of Collet-Epstein-Gallovotti, Moore, and Ratner for hyperbolic surfaces. Furthermore, since the analysis is even easier in three dimensions than in two dimensions (because of the absence of discrete series and the simplicity of the zonal spherical functions in this case), this apparently gives the simplest example of a flow with exponential mixing.     

On the Integrability of Geodesic Flows of Submersion Metrics

Letters in Mathematical Physics - Suppose we are given a compact Riemannian manifold (Q,g) with a completely integrable geodesic flow. Let G be a compact connected Lie group acting freely on Q by...     

导波声光频谱仪集成光路的研究

根据频率分辨率极限和光学分辨经极限，用解析理论的精确公式设计了导波声光频谱仪集成光路，用单点金刚石超精加工和凹面波导制备工艺，研制成Φ１２ｍｍ双孔非球面短程透镜型导波声光频谱仪民集成光路芯片，实验结果表明，器件集成光路在８ｍｍ宽输入光束下通光性能良好，双孔非球面透镜的镜的焦点分别在左，右两端面上，且输出端面焦点衍射光斑半功率点宽度≤４μｍ。     

Kerr-Newman黑洞隧穿辐射的新研究

在文章[吴迪等2013中国科学物理学力学天文学43115]中,从有质量粒子的Lagrangian作用量出发,对Kerr转动黑洞中类时的和类光的测地线方程给出了全新的统一推导,结果表明对转动黑洞隧穿辐射的研究不需要局限地采用拖曳系.这项工作完全克服了先前研究中存在的不足,使得Parikh-Wilczek半经典隧穿方法更加完善和自洽.本文将这一工作推广到转动带电黑洞情形,对Kerr-Newman黑洞中有质量带电粒子测地线方程做了新的推导,并对其隧穿辐射重新做了研究.