非对易OrbifoldR4/G上的量子态及孤子解

求得二维由广义坐标和广义动量构成的一般二次型哈密顿量的基态,由此可以求得各能级的本征态.由于四维非对易空间在转动群GSO(4)下的坐标的不变二次型可以正则化为这类哈密顿量,因此得到了非对易空间R4上转动不变的态矢量.当G是SO(4)的有限子群时候它们是R4/G这种非对易Orbifold上的态矢量.由此可以得到其上的孤子解.     

三维晶体学群的极大有限群的代数基础

从NTN=T这一晶体学的普遍公式出发,推导出在三维空间中度量张量矩阵T有四个算术不等价类,即公式见正文,而T₁,T₃,T₄属几何等价类,故几何不等价类只有T₁及T₂.根据NT₁ N=T₁及NT₂ N=T₂求出三维晶体学的两个极大有限群分别为48阶及24阶,它们对应于两个晶体学点群,其他三十个点群则可通过母子群网 关键词： 晶体学 对称群 有限群     

强子同位旋的有限群分类

杨振宁等人很早就建议采用三维旋转群的有限子群来对强子同位旋进行分类。最近文献[2]又继续进行了讨论。这些处理尽管容易得到强子同位旋具有确定上限的结论,但是还存在着一些尚待解决的问题。例如,这些作者都是用有限群对强子直接分类,往往不得不把介子和重子分别填入不同有限群的不可约表示。显然这在处理介子与重子之间的相互作用问题时会遇到困难,对于如何确定强子的量子数等问题,也有不清楚的地方。     

用SU(2)的分立子群对SU(2)格点规范新作用量的Monte Carlo 模拟

我们用SU(2)的正二十面体分立子群对SU(2)格点规范理论的正弦作用量与指数作用量进行了Monte Carlo模拟。发现由分立子群本身产生的一阶相变点分别在β_c′≈9.2±0.2和β_c′=6.8±0.2。对方格能量和比热所得的结果与用SU(2)群所得的结果一致。从而证实了对以上两种作用量,用分立子群代替连续群的适用性,为以后进行计算时利用分立子群提供了依据。 关键词：     

碳纳米管中的群论及一系列新点群

在讨论了碳纳米管的几何结构的基础上，对齿型和椅型碳纳米管的对称性进行了分析并将这些对称元进行了抽象和总结.对齿型和椅型碳纳米管的对称元所属的群Dnh点群进行了讨论. 关键词： 点群 碳纳米管 几何结构 对称性     

晶体学与准晶体学点群的母子群关系

依据群论，得出了准晶体学点群的直积或半直积推导算式；依据结晶学理论，绘出了五角、八角、十角和十二角晶系各点群的极赤投影图.据此推导出了每一个准晶体学点群的全部最大子群，从而推导并绘制出了三维晶体学和准晶体学点群之间的母子群关系(60个点群的“家谱”).该“家谱”以最大子群链的图解形式直观地给出了每个点群的最小母群和最大子群. 关键词： 准晶体 晶体 点群 最大子群 最小母群 群链     

基于大规模并行计算的三维多群中子扩散方程有限差分方法

三维多群中子扩散方程的精确、高效求解是核动力堆芯设计及燃料管理的基础。应用有限差分方法求解该方程具有简便、精确、成熟的优点;然而,该方法的计算量和存储量均较大,极大地限制了它的计算规模和应用范围。本文基于大规模并行计算,研究三维多群中子扩散方程有限差分方法:采用中心有限差分格式离散中子扩散方程;基于MPI并行编程模型,采用空间区域分解的方式实现大规模并行计算;采用多群多区域耦合PGMRES算法进行并行加速。在集群服务器上开发了ParaFiDi程序,并采用IAEA3D,PHWR等多个基准题对该程序进行验证。数值结果表明,ParaFiDi程序具有较高的计算精度和计算效率。     

Ih点群及其在分子振动谱分析中的应用

系统介绍了Ｉｈ点群的对称操作、类和不可约特征标表。给出了Ｉｈ群及其主要子群的相适关系表。应用Ｉｈ群对Ｈ１３，Ｃ２０Ｈ２０和Ｃ６０分子振动谱的红外活性和拉曼活性进行了分析。     

三粒子系统的物理基

本文利用SO(6)和SU(4)局部同构性质以及SU(3)群的正则子群链与物理子群链之间的变换系数, 构造出了三个全同粒子系统内部的物理基, 并指出这个基与Aguila的超球函数基是一致的.     

一种超材料梁对机械波振动吸收的模拟研究

本文设计了一种能够对机械波进行吸收的超材料梁,超材料梁由若干质量-弹簧微结构系统和一根各向同性梁构成.通过对两种不同结构的质量-弹簧系统的分析,从理论上解释了"负有效质量"和"负有效刚度".根据Hamilton原理,导出了超材料梁的代表性胞元的控制方程.通过数值模拟分析了两种不同结构的有限超材料梁对机械波的吸收性能,一种是弹性系数线性变化的质量-弹簧系统在有限梁内均匀分布,另一种是由固有频率线性变化的弹簧-阻尼器子系统构成四个相同吸收器子群在有限梁内均匀分布.模拟结果表明,进入梁中的机械波与质量-弹簧振子 关键词： 超材料梁 负有效质量 负有效刚度 机械波     

On Euler–Arnold equations and totally geodesic subgroups

The geodesic motion on a Lie group equipped with a left or right invariant Riemannian metric is governed by the Euler–Arnold equation. This paper investigates conditions on the metric in order for a given subgroup to be totally geodesic. Results on the construction and characterisation of such metrics are given, especially in the special case of easy totally geodesic submanifolds that we introduce. The setting works both in the classical finite dimensional case, and in the category of infinite dimensional Fréchet–Lie groups, in which diffeomorphism groups are included. Using the framework we give new examples of both finite and infinite dimensional totally geodesic subgroups. In particular, based on the cross helicity, we construct right invariant metrics such that a given subgroup of exact volume preserving diffeomorphisms is totally geodesic.     

Lie algebras and representations of continuous groups

It is shown that every finitely generated continuous group has a subgroup generated by its infinitesimal transformations. This subgroup has a group algebra which is the Lie algebra of the group. By obtaining complete systems in the Lie algebra and complete rectangular arrays, it is shown that these can yield matrix representations of the continuous group. Illustrative examples are given for the rotation groups and for the full linear groups. It would seem that all the finite motion representations can be obtained by these methods, including spin representations of rotation groups. But the completeness of the method is not here demonstrated.     

Role of Dilations in Diffeomorphism-Covariant Algebraic Quantum Field Theory

A generalization of algebraic quantum field theory on differentiable manifoldsis given in terms of nets of *-algebras over open sets of the manifold. The presentinvestigations are motivated by diffeomorphism invariance and finite localizationas they appear, e.g., in quantum gravity. A possible generalization of Haag-Kastleraxioms for differentiable manifolds is discussed and a minimal framework basedon isotony, covariance, and a state-dependent GNS construction is presented.Possible adaptions of Haag's commutant duality are discussed in a specific settingof one-parameter families of finite and nondegenerate nested localization domainsof the net, with universal minimal and maximal algebras for the small and largelimits of the net, respectively. For von Neumann algebras the modular group isdiscussed. The geometric interpretation of a one-parameter subgroup of outerisomorphisms is related to dilations of the open sets of the net.     

Norms in group algebras of finite groups under inducing

We compare norms of an element of a group algebra of a normal subgroup of a finite group in a representation of the normal subgroup and the corresponding induced representation (under the natural embedding of the group algebra of the normal subgroup in the group algebra of the entire group).     

Lyapunov Bounds for Lattice Gauge Dynamics

We study the classical Hamiltonian dynamics of the Kogut–Susskind model for lattice gauge theories on a finite box in a d-dimensional integer lattice. The coupling constant for the plaquette interaction is denoted λ². When the gauge group is a real or a complex subgroup of a unitary matrix group U(N), N≥ 1, we show that the maximal Lyapunov exponent is bounded by , uniformly in the size of the lattice, the energy of the system as well as the order, N, of the gauge group. Received: 20 December 1997 / Accepted: 21 July 1998     

On a method of constructing irreducible multiplier representations

A systematic method is presented for constructing the irreducible multiplier representations (ray representations) of a class of finite groups corresponding to a given factor system. The method consists in first identifying a normal subgroup of prime index, classifying its irreducible multiplier representations into orbits and then inducing the required representations from these orbits. The proposed technique finds useful application in solid state physics where irreducible multiplier representations of the point group underlying the group of the wave vector are frequently required.     

Classical Dynamical r-Matrices¶and Homogeneous Poisson Structures on G/H and K/T

Let G be a finite dimensional simple complex group equipped with the standard Poisson Lie group structure. We show that all G-homogeneous (holomorphic) Poisson structures on G/H, where H⊂G is a Cartan subgroup, come from solutions to the Classical Dynamical Yang–Baxter equations which are classified by Etingof and Varchenko. A similar result holds for a maximal compact subgroup K, and we get a family of K-homogeneous Poisson structures on K/T, where T=K∩H is a maximal torus of K. This family exhausts all K-homogeneous Poisson structures on K/T up to isomorphisms. We study some Poisson geometrical properties of members of this family such as their symplectic leaves, their modular classes, and the moment maps for the T-action. Received: 4 September 1999 / Accepted: 25 January 2000     

Quantum Mechanics on Finite Groups

Although a few new results are presented, this is mainly a review article on the relationship between finite-dimensional quantum mechanics and finite groups. The main motivation for this discussion is the hidden subgroup problem of quantum computation theory. A unifying role is played by a mathematical structure that we call a Hilbert ^*-algebra. After reviewing material on unitary representations of finite groups we discuss a generalized quantum Fourier transform. We close with a presentation concerning position-momentum measurements in this framework.