三维非谐势阱中玻色-爱因斯坦凝聚的数值计算

本文从G-P平均势场理论出发,探讨了三维球对称非谐势阱中玻色-爱因斯坦凝聚(BEC)的G-P方程;用数值计算方法研究了三维球对称非谐势阱中原子间有相互作用的玻色-爱因斯坦凝聚气体的基态解;分析了非谐振势能项对玻色-爱因斯坦凝聚体的分布、能量和化学势的影响.     

《广义相对论入门讲座》连载⑧——广义相对论的实验验证

1 史瓦西解史瓦西给出了爱因斯坦方程的一个严格解,这是一个静止、球对称星体外部的真空解,其中不为零的度规分量为     

复合电磁同心球系统的成像电子光学. D章:近轴方程渐近解（英文）

首次探讨了复合电磁同心球系统近轴方程的渐近解。推导了复合电磁同心球系统中近轴方程两个特解的渐近解中各类系数的表达式。通过复合电磁同心球系统两个特解精确解的验证,证明了Monastyrski[Journal of Technical Physics,1978,48(6):1117-1122]提出的用渐近解求解成像电子光学近轴方程两个特解的方法正确且可行,仅个别之处需要改进。     

三维非谐势阱中玻色－爱因斯坦凝聚的数值计算

本文从G－P平均势场理论出发,探讨了三维球对称非谐势阱中玻色－爱因斯坦凝聚(BEC)的G－P方程;用数值计算方法研究了三维球对称非谐势阱中原子间有相互作用的玻色－爱因斯坦凝聚气体的基态解;分析了非谐振势能项对玻色－爱因斯坦凝聚体的分布、能量和化学势的影响。     

球对称非谐势阱中玻色-爱因斯坦凝聚Gross-Pitaevskii方程的精确解

考虑了描述玻色 爱因斯坦凝聚的Gross-Pitaevskii(GP)方程, 得到了在球对称非谐势阱中玻色-爱因斯坦凝聚GP方程的精确亮孤子解。In this paper, we analyze Gross Pitaevskii equation which describes the dynamics of a bright soliton in trapped atomic Bose Einstein condensates, and obtain the exact bright soliton solution of Gross Pitaevskii equation in spherically symmetric non harmonic trap.     

玻色子多体系统的平均场理论:玻色-爱因斯坦凝聚体(BEC)的冷却与激发

用量子主方程的平均场近似和代数动力学研究玻色-爱因斯坦凝聚体的sympathetic cooling; 用玻色-爱因斯坦凝聚体波函数的运动方程的平均场近似 非线性薛定谔方程研究玻色 爱因斯坦凝聚体的暗孤子和明孤子激发.     

相对论热力学向量理论对Schwarzschild场中物质系统特性的研究

应用相对论热力学向量理论，讨论了Ｓｃｈｗａｒｚｓｃｈｉｌｄ场中球对称静态理想流体恒星结构，得到了Ｔｏｌｍａｎ-Ｏｐｐｅｎｈｅｉｍｅｒ-Ｖｏｌｋｏｆ方程，并且就该引力场中粒子系统的不同运动状况做了讨论，由此得到了与经典极限相符合的结果．     

SU(2)规范理论中标量场方程的球对称解

本文用幂级数方法给出了非线性场方程(?)全部的球对称的严格解,方程的球对称通解只有三种:(?)     

复合电磁同心球系统的成像电子光学. C章:近轴方程近似解（英文）

通过复合电磁同心球系统的理想模型,探讨了近轴方程特解的近似表示及其近轴横向像差的求解。导出了复合电磁同心球系统近轴方程两个特解的近似表达式,在此基础上导出了一些特殊类型的近轴横向像差的表达式,如近轴色球差、近轴放大率色差和近轴各向异性色差。结果表明,由两个特解的近似解推导得到的近轴横向像差与使用精确解的结果完全一致,由此证明近似解求解近轴横向像差的方法是可行的。     

非谐势阱中玻色-爱因斯坦凝聚的数值计算

从G-P平均势场理论出发,探讨了玻色-爱因斯坦凝聚(BEC)的G-P方程的一维形式,用数值计算方法研究了非谐势阱中非理想玻色凝聚气体的基态和第一激发态解.给出了能量随非线性系数的变化规律.     

两类非线性方程的精确解

利用行波约化方法，并借助于一维立方非线性Klein-Gordon方程的精确解，求出了（1+1）维Zakharov方程组、变系数Korteweg-de Vries方程的一些精确解- 关键词： 行波约化方法 一维立方非线性Klein-Gordon方程 （1+1）维Zakharov方程组 变系数Korteweg-de Vries方程     

Interior Schwarzschild Problem and Its Integration

The interior Schwarzschild metric for a static,spherically symmetric perfect fluid can be parametrizedwith two independent functions of the radial coordinate.These functions are easily expressed in terms of (radial) integrals involving the fluidenergy density and pressure. The pressure is, however,not independent, but is determined in terms of thedensity by one of Einstein's equations, theOppenheimer–Volkov (OV) equation. An approximate integral to theOV equation is presented which is accurate for slowlyvarying, realistic, densities, and exact in theconstant-density limit. It makes it possible to findcompletely integrated accurate solutions to the interiorSchwarzschild metric in terms of the density only. Somepost-Newtonian consequences of the solution are given aswell as the resulting general relativistic pressure for an energy densityr^-1/2.     

MKdV方程的拟小波解

用拟小波方法求MKdV方程的数值解-先用拟小波离散格式离散空间导数，然后用四阶Runge-Kutta方法离散时间导数,对一个有精确解的实例ut+6u2ux+uxxx=0进行了数值计算-拟小波解与解析解完全重合，t=10000s时，二者也没有偏差- 关键词： MKdV方程 拟小波方法 孤子解     

一维强场模型研究中的非齐线性正则方程的辛算法

就一维强场模型,采用对称差商代替空间变量的2阶偏导数,将含有SchrÖdinger方程的初边值问题离散成"非齐线性正则方程",它的齐方程的通解和非齐方程特解都由"辛变换生成",分别采用辛格式计算.采用这种辛算法和R-K法计算了一个数值例子,并与精确解作了比较.结果表明,经长时间计算后,辛算法保持解的固有特征,而R-K法则面目全非.     

Static circularly symmetric perfect fluid solutions with an exterior BTZ metric

In this work we study static perfect fluid stars in 2+1 dimensions with an exterior BTZ spacetime. We found the general expression for the metric coefficients as a function of the density and pressure of the fluid. We found the conditions to have regularity at the origin throughout the analysis of a set of linearly independent invariants. We also obtain an exact solution of the Einstein equations, with the corresponding equation of state p = p(), which is regular at the origin.     

Dust and radiation quantum perfect fluid cosmology: selection of time variable

We studied the expectation value of the scale factor in radiation and dust quantum perfect fluid cosmology. We used Schutzs variational formalism to describe the perfect fluid and selected the conjugate coordinate of the perfect fluid to be the dynamical variable. After quantization and solving the Wheeler-DeWitt equation we obtained an exact solution. By superposition of exact solutions, we obtained one wave packet and used it to compute the expectation value of the scale factor. We found that if one selects a different dynamical variable being the time variable in each of these two systems, the expectation value of the scale factor of these two systems can fit in with the prediction of General Relativity. Therefore we thought that the selection of a reference time can be different for different quantum perfect fluid systems.     

Perfect fluid spheres in general relativity

Spherically symmetric perfect fluid distributions in general relativity have been investigated under the assumptions of (i) uniform expansion or contraction and (ii) the validity of an equation of state of the formp=p(ρ) with nonuniform density. An exact solution which is equivalent to a solution found earlier by Wyman is obtained and it is shown that the solution isunique. The boundary conditions at the interface of fluid distribution and the exterior vacuum are discussed and as a consequence the following theorem is established:Uniform expansion or contraction of a perfect fluid sphere obeying an equation of state with nonuniform density is not admitted by the field equations. It is further shown that the Wyman metric is not suitable on physical grounds to represent a cosmological solution.     

Gravitational Collapse of Self-Similar Perfect Fluid in 2 + 1 Gravity

Perfect fluid with kinematic self-similarity is studied in 2+1 dimensional spacetimes with circular symmetry, and various exact solutions to the Einstein field equations are given. These include all the solutions of dust and stiff perfect fluid with self-similarity of the first kind, and all the solutions of perfect fluid with a linear equation of state and self-similarity of the zeroth and second kinds. It is found that some of these solutions represent gravitational collapse, and the final state of the collapse can be either a black hole or a null singularity. It is also shown that one solution can have two different kinds of kinematic self-similarity.     

Newtonian stellar models

We investigate static spherically symmetric perfect fluid models in Newtonian gravity for barotropic equations of state that are asymptotically polytropic at low and high pressures. This is done by casting the equations into a three-dimensional regular dynamical system with bounded dependent variables. The low and high central pressure limits correspond to two two-dimensional boundary subsets, described by homology invariant equations for exact polytropes. Thus the formulation naturally places work about polytropes in a more general context. The introduced framework yields a visual aid for obtaining qualitative information about the solution space and is also suitable for numerical investigations. Moreover, it makes a host of mathematical tools from dynamical systems theory available, which allows us to prove several theorems about the relationship between the equation of state and properties concerning total masses and radii.