准周期层状铁磁超晶格的实空间重整化群方法

本文用实空间重整化群方法讨论了准周期层状铁磁超晶格的磁自旋波,用Reduce语言推导了decimation变换公式,从而求得了局域格林函数、局域态密度和约化磁矩。发现局域态密度的带宽和约化磁矩与最近邻相互作用J₁、J₂及格点自旋s_a、s_b密切相关。     

提高重整化群精度的一个尝试

以热逾渗分析散粒体导热率时,利用重整化群方法改变粗视化程度来定量地获得导热率的变化。实践表明这只有设法提高重整化群的精度才会有较好的结果。本文以逾渗转变为例,针对b=2的相关尺度变化方式,分别对二维和三维实空间的重整化变换进行了修正,导出了相应的重整化方程。计算精度有明显提高,计算结果与实验值更接近。     

纳米结构链的hopping电导实空间重正化群方法

基于Miller-Abrahams理论,发展了一种重正化群方法,研究了一维纳米结构体系的hopping电导.研究表明在纳米结构体系中晶粒种类、晶粒尺寸对hopping电导有显著的调制作用,界面结构及晶格畸变等对hopping电导也有不同程度的影响.     

ON THE EFFECTIVE LAGRANGIAN FOR THE PURE SUPER YANG-MILLS THEORY DERIVED FROM RENORMALIZATION GROUP CONSIDERATIONS

Further comments and analysis are made on the derivation of the effective Lagrangian for the N=1 pure super Yang-Mi11s theory from renormalization group considerations and on the implications of results obtained.     

IMPROVEMENT ON THE MIGDAL-KADANOFF RENORMALIZATION TRANSFORMATION

A migdal-Kadanoff transformation is improved by using the mean-field approximation to find the relation between the coupling constants of the restructured lattice and the on ginal one.Calculations of the critical coupling and exponents for the Ising model showed much improvement, even for small clusters, compared with the results of MK calculations.     

非均匀无序系统中Anderson局域化的标度理论——实空间重整化群途径

针对大量具有空间调制的无序系统,本文提出一种实空间重整化群变换方案。这个方案保证了在空间映象下相对的空间调制结构不变,因此可用以研究非均匀无序系统Anderson局域化的临界性质。在有限晶格近似下,我们对无序金属超晶格的一个简化模型求解了RG方程,得到不动点和临界指数的近似值,并发现空间调制在一定程度上引起无序系统电子局域化性质的改变。 关键词：     

逾渗的计算机模拟实验

本介绍了一个分析逾渗问题的CAI软件,应用该软件可对二维几何相变进行计算机模拟实验,从而了解逾渗系统的物理特性和规律。     

A GROUP THEORETIC APPROACH TO THE LINEAR FREE VIBRATION ANALYSIS OF SHELLS WITH DIHEDRAL SYMMETRY

This paper deals with a group theoretic approach to the finite element analysis of linear free vibrations of shells with dihedral symmetry. Examples of such shell structures are cylindrical shells, conical shells, shells with circumferential stiffeners, corrugated shells, spherical shells, etc. The group theoretic approach is used to exploit the inherent symmetry in the problem. For vibration analysis, the group theoretic results give the correct symmetry-adapted basis for the displacement field. The stiffness matrix K and the mass matrix M are identically block diagonalized in this basis. The generalized linear eigenvalue problem of free vibration gets split into independent subproblems due to this block diagonalization. The Simo element is used in the finite element formulation of the shell equilibrium equations. Numerical results for natural frequencies and natural modes of vibration of several dihedral shell structures are presented. The results are shown to be in very good agreement with those reported in the literature. The computational advantages and physical insights due to the group theoretic approach are also discussed.     

群表示论的物理方法(Ⅰ)——有限群表示论的新途径

本文介绍一种完全用量子力学中对易算符集方法处理的有限群表示论。把群表示论中的基本问题,如计算特征标,不可约基,不可约矩阵元和CG系数等都归结为求完备算符集的本征值和本征函数。     

人工智能研究的物理学途径

近年来,人工智能研究的物理学途径已越来越受到人们的关注,这一途径的实现方式主要有两种：一是把已有的物理理论和方法直接用于研究计算系统,以达到对计算系统的性质和规律的认识,另一是依据某些计算系统与物理的相似性,把计算问题转换为对应的物理问题,再用物理方法建构有效的算法加以求解,文章着重介绍运用物理学途径研究计算系统的相变和解决多自主体系统的目标满足问题所取得的进展,并指出了这一途径的优点和应该注意的问题。     

二维随机三角点阵上三态和四态Potts模型的蒙特—卡罗重整化群研究

本文用改进的蒙特-卡罗重整化群方法对二维随机三角点阵上的三态和四态Potts模型进行研究,分析它们的固定点及临界指数,所得的临界指数与理论的分析值符合很好。     

DLA模型的最可几方法研究

用最可几方法对DLA模型进行了研究，求出了DLA集团粒子的最可几分布、分维数和屏蔽指数，所得结果与计算机模拟结果相符合 关键词：     

用人工神经网络计算双原子分子的键长

用神经网络反向传播算法计算了双原子分子的键长。采用二原子的Slater原子半径,Paul-ing电负性,在元素周期表中的主族数及周期数等作为特征变量,得到了神经网络的训练及预报结果。     

THE LOOP PHASE-FACTOR APPROACH TO GAUGE FIELDS

The gauge field theory is formulated via loop phase factors with a fixed point O as their initial and final point. Let G be the gauge group. When the base space is the Minkowski space E₄, we introduce a set of standard paths Ox （for example, the set of line segments Ox）, where x is arbitrary. The phase factor for the infinitesimal loop Oxx+dxO corresponds to an element in the Lie algebra g and can be expressed as a g-valued differential form k（x, dx） which satisfies the following conditions of consistency （a） k（O, dx）=0, （b） k（x, v）=0, where v is the tangential vector of Ox at x. It is shown that an equivalent class of gauge fields is determined by k（x, dx） or （ad a） k（x, dx） where a is a fixed element of G. Hence if we adopt k（x, dx） for the fundamental physical quantity of a gauge field then a great part of gauge indefiniteness is eliminated. Moreover if the phase factors Φ_xo for standard paths Ox are given then the phase factors for differential arcs x x+dx are easily calculated, and hence a gauge field in the equivalent class is extracted. We call the set of phase factors for standard paths a gauge and k（x, dx） may be interpretated as the gauge potential under a special gauge under which Φ_xo=the unit element of G.The method is useful in considering the equivalence problem and the spacetime symmetry of gauge fields. For example, it is quite easy to determine all spherically symmetric gauge fields if they are free of singularities. By using the method it can also be proved that if two gauge fields have the same gauge and the same field strength then their gauge potentials are equal to each other. Consequently, under a given gauge in the above sense the field strength determines the gauge potential completely.For a general base manifold M_n, every equivalent class of gauge fields over M_n can be defined by loop phase factors also. In this case, M_n is expressed as the sum of a set of neighborhoods each of which is homeomorphic to the Euclidean space. The standard paths are constructed according a certain rule, the phase factors for standard differential loops are also introduced. The transition functions and gauge potentials of a gauge field in the given equivalent class are derived as the phase factors for some finite loops and standard differential loops respectively. Further it is remarkable that a global gauge field is determined completely by the field strength and some discrete loop factors, if the phase factors for the standard paths are gwen.In mathematical terminology principal G-bundle structure as well as a connection in it is determined by the holonomic mapping which maps the set of loops through a fixed point into the group G, provided the mapping is differentible in a certain.The author is very grateful to Prof. Yang Chen Ning for many helpful discussions.     

光能够走多慢?——极慢光速研究若干进展

首先介绍了光波群速度，介质的色散性质，电磁感应透明技术等基本概念和理论，对国外极慢光速研究的进展情况做了概括性介绍，并就几个主要实验及结果进行了较为详细的描述，其中包括L.V.Hau小组于1999年完成的“光速每秒17m”实验和D.F.Phillips小组于2001年发表的“在原子气中储存光”实验，文章最后就极慢光速研究在科学和应用两方面的意义及价值进行了讨论。     

关于复合粒子量子场论的重整化理论和红外发散消去问题

量子电动力学以及量子场论的重整化理论的建立已经近三十年了。但包含复合粒子的跃迁、产生、湮灭等过程的辐射修正的计算问题却没有很好解决。近来,由于复合粒子场论的研究有一些进展,这就又提出了对复合粒子体系如何重整化以及如何消去红外发散的问题。     

AN APPROACH TO THE STRUCTURE FUNCTION FOR UNCLEON

The structure function for nucleon is discussed by using the method given in a previous paper. The formula are compared with the experimental data from low Q² to high Q². The results show that the way that the structure function for nucleon can be obtained from the hadronic wavefunction is a possible approach of investigating structure functions for hadron.     

关于状态分立系统的改进的Metropolis方法

对状态分立系统的平衡态统计问题给出了一个改进的Metropolis方法,并在伊辛模型上与传统方法进行了对比,得到了一致的结果,效率提高了约25%.针对伊辛模型的抽样过程给出了其马尔科夫过程所对应的Master方程.将所提出的方法应用于伊辛模型,相当于对其Master方程进行了模拟.作为推广,一大类临界动力学模型的Master方程都可以用本方法进行模拟,以用于其暂态过程的研究.