共形场论和相变

本文讨论了共形对称性,量子共形对称理论以及相变现象。讨论了二维共形场论中最基本的自由玻色场和费米场,也介绍了玻色化、高斯泛函、ＳＧ模型及其简单应用     

一个正规化方案及弦理论中的共形反常

本文建议一个改进的正规化方法;并讨论玻色弦以及超弦的共形反常.     

Barriola-Vilenkin黑洞的统计熵

利用量子统计方法 ,直接计算Barriola_Vilenkin黑洞背景下玻色场和费米场的配分函数 ,然后利用砖墙膜模型计算和讨论黑洞背景下玻色场和费米场的熵     

Barriola-Viienkin黑洞的统计熵

利用量子统计方法,直接计算Barriola-Vilenkin黑洞背景下玻色场和费米场的配分函数,然后利用砖墙膜模型计算和讨论黑洞背景下玻色场和费米场的熵.     

玻色超共形Toda模型与Dressing变换

本文从玻色超共形Toda模型的经典γ矩阵出发,研究各种场量以及经典手征算子在Dressing变换下的性质,并且得到相应的量子代数.     

Kerr-Newman-de Sitter黑洞的统计熵

避开求解波动方程的困难，利用量子统计的方法，直接计算Kerr-Newman-de Sitter黑洞背景下玻色场和费米场的配分函数.然后利用砖墙膜模型计算和讨论黑洞背景下的玻色场和 费米场的熵. 关键词： 量子统计 砖墙膜模型 Kerr-Newman-de Sitter黑洞 统计熵     

一维自旋-1/2XY模型的磁场效应

本文主要利用Haldane的谐振流理论——玻色化方法研究外场中的自旋-1/2XY模型。本文首先将无磁场情况下该模型的哈密顿进行了玻色化与对角化,并单独讨论了磁场项,最后两者联合给出外磁场中一维自旋-1/2模型哈密顿的玻色化形式。在这种形式下哈密顿量中的协变问题可以通过平移费米点来解决,所以,在阿贝尔玻色化方案下对玻色场算符做了重新定义,得到一个新的协变的哈密顿,从而解决了由于扰动所带来的问题,各关联函数也随之给出;最后简单讨论了平移费米点给模型关联函数的表达式带来的变化,以及玻色化方法较之其他方法的优长。     

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.     

囚禁弱相互作用玻色气体的势场优化准则

根据Thomas-Fermi近似,在基于最小动量态上玻色-爱因斯坦凝聚的前提下,研究了囚禁弱相互作用玻色气体势场的最优化问题.导出了指数吸引势阱中有效势场和粒子数极限判据,粒子数给定时,可由此判据求出所需势场强度;势场强度给定时,可由此判据求出粒子数极限.根据吸引相互作用系统的稳定性以及求出的排斥相互作用的最大粒子数极限,结合有效势场判据,分别给出了囚禁吸引和排斥相互作用玻色气体时,势场强度的最佳取值范围. 关键词： 玻色-爱因斯坦凝聚 弱相互作用 粒子数极限 势场强度     

虚光场对双模SU(1,1)相干态光场与原子玻色-爱因斯坦凝聚体相互作用系统中量子纠缠的影响

在双模SU(1,1)相干态光场和原子玻色-爱因斯坦凝聚体相互作用系统中, 应用全量子理论, 在非旋波近似下, 分别利用量子约化熵和量子相对熵, 研究了双模SU(1,1)相干态光场与原子玻色-爱因斯坦凝聚体间的量子纠缠和双模光场的模间纠缠, 讨论了虚光场、原子-场的耦合常数和光场参数对场-凝聚体原子纠缠和光场模间纠缠的影响.     

Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems

In this paper, the relation of the conformal invariance, the Noether symmetry, and the Lie symmetry for the Hamilton system is discussed in detail. The definition of the conformal invariance for Hamilton systems is given. The relation between the conformal invariance and the Noether symmetry is discussed, the conformal factors of the determining expressions are found by using the Noether symmetry, and the Noether conserved quantity resulted from the conformal invariance is obtained. The relation between the conformal invariance and the Lie symmetry is discussed, the conformal factors are found by using the Lie symmetry, and the Hojman conserved quantity resulted from the conformal invariance of the system is obtained. Two examples are given to illustrate the application of the results.     

Conformal groups and conformally equivalent isometry groups

It is shown that if ann dimensional Riemannian or pseudo-Riemannian manifold admits a proper conformal scalar, every (local) conformal group is conformally isometric, and that if it admits a proper conformal gradient every (local) conformal group is conformally homothetic. In the Riemannian case there is always a conformal scalar unless the metric is conformally Euclidean. In the case of a Lorentzian 4-manifold it is proved that the only metrics with no conformal scalars (and hence the only ones admitting a (local) conformal group not conformally isometric) are either conformal to the plane wave metric with parallel rays or conformally Minkowskian.     

Complete Classification of Conformal Killing Symmetries of Plane-Symmetric Static Spacetimes in Teleparallel Theory

We have studied the conformal, homothetic and Killing vectors in the context of teleparallel theory of gravitation for plane-symmetric static spacetimes. We have solved completely the non-linear coupled teleparallel conformal Killing equations. This yields the general form of teleparallel conformal vectors along with the conformal factor for all possible cases of metric functions. We have found four solutions which are divided into one Killing symmetries and three conformal Killing symmetries. One of these teleparalel conformal vectors depends on x only and other is a function of all spacetime coordinates. The three conformal Killing symmetries contain three proper homothetic symmetries where the conformal factor is an arbitrary non-zero constant.     

Conformal Invariance and Noether Symmetry,Lie Symmetry of Birkhoffian Systems in Event Space

This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigation on the relations between the conformal invariance and the Noether symmetry, the conformal invariance and the Lie symmetry, the expressions of conformal factors of the system under these circumstances are obtained. The Noether conserved quantities and the Hojman conserved quantities directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.     

Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems

This paper studies conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems. Third-order Lagrange equations, the definition and a determining equation of conformal invariance of the system are presented. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The necessary and sufficient condition that conformal invariance of the system would have Lie symmetry under single-parameter infinitesimal transformations is obtained. The corresponding conserved quantity of conformal invariance is derived with the aid of a structure equation. Lastly, an example is given to illustrate the application of the results.     

Conformal invariance and conserved quantities of Birkhoff systems under second-class Mei symmetry

This paper proposes a new concept of the conformal invariance and the conserved quantities for Birkhoff systems under second-class Mei symmetry.The definition about conformal invariance of Birkhoff systems under second-class Mei symmetry is given.The conformal factor in the determining equations is found.The relationship between Birkhoff system’s conformal invariance and second-class Mei symmetry are discussed.The necessary and sufficient conditions of conformal invariance,which are simultaneously of second-class symmetry,are given.And Birkhoff system’s conformal invariance may lead to corresponding Mei conserved quantities,which is deduced directly from the second-class Mei symmetry when the conformal invariance satisfies some conditions.Lastly,an example is provided to illustrate the application of the result.     

Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space

This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding conformal factors of the holonomic system in event space are given. By investigating the relation between the conformal invariance and the Noether symmetry and the Lie symmetry, expressions of conformal factors of the system under these circumstances are obtained, and the Noether conserved quantity and the Hojman conserved quantity directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.     

Conformal invariance and conserved quantities of general holonomic systems in phase space

This paper studies the conformal invariance and conserved quantities of general holonomic systems in phase space. The definition and the determining equation of conformal invariance for general holonomic systems in phase space are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The relationship between the conformal invariance and the Lie symmetry is discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal single-parameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.     

变质量完整系统的共形不变性和Noether对称性及Lie对称性

研究变质量完整系统在无限小变换下的共形不变性与Noether对称性和Lie对称性.首先,给出了变质量完整系统的共形不变性的定义;其次,研究了系统的共形不变性与Noether对称性之间的关系,得到了共形不变性导致的Noether守恒量;最后,研究了系统的共形不变性与Lie对称性之间的关系,得到了共形不变性同时是Lie对称性导致的Hojman守恒量.最后举例说明了结果的应用.     

Aerodynamic heating of the dome on imaging quality degradation of conformal optical systems

The aerodynamic flow field surrounding the conformal dome was calculated. The thermal response of the aerodynamically heated conformal dome was analyzed. Gradient refractive index method was used to rebuild the non-uniform refractive index field of the conformal dome. Zernike polynomial fitting method was employed to establish the deformed surfaces of the conformal dome. Zernike aberration theory and modulation transfer function were adopted to evaluate the imaging quality of the conformal optical system. The results show that the aerodynamic heating of the dome severely affects the imaging quality of the conformal optical system.