管状和闭合磁畴壁的拓扑分类

本文从拓扑学角度,对管状磁畴壁和闭合磁畴壁静态结构的分类问题,做了统一处理。这两种磁畴壁的同伦类集合G_W⁽ⁿ⁾和G_W⁽ⁿ⁾,分别与S²→S²和S³→S²的n+1基点连续映射的相对同化类集合是一一对应的,因而构成同构于整数加群Z的群,分别称为n式管壁群和n式闭壁群。重新讨论了Slonczewski等人定义的“绕数”,找出了用它表征管壁 关键词：     

多基点同伦群理论

本文建立了一个定理:当拓扑空间V单连通时,N(≥1)基点n阶同伦类集合π_n(V;v₁,v₂,…,v_N)可被构造成同构于单基点n阶同伦群π_n(V)的群,叫做N基点n阶同伦群;并且V的单连通性一般是不可省略的条件。给出了一些推论。简要地触及了这个定理及其推论在铁磁状态拓扑分类中的应用问题。 关键词：     

二维超导薄膜中拓扑缺陷数目与冷却速度关系研究

基于含时Ginzburg-Landau（TDGL）方程建立二维超导薄膜经历快速冷却后的拓扑缺陷数目与冷却速度的关系模型.采用差分法对此模型进行了数值模拟,计算出不同冷却速度下拓扑缺陷数目随着时间的变化关系.计算结果发现,在不同冷却速度下,缺陷数目随着时间的变化可以分为两个阶段：第一阶段缺陷数目较多,拓扑缺陷数目随时间急...     

Homotopy Classification of Bosonic String Field Theory

We prove the decomposition theorem for the loop homotopy Lie algebra of quantum closed string field theory and use it to show that closed string field theory is unique up to gauge transformations on a given string background and given S-matrix. For the theory of open and closed strings we use results in open-closed homotopy algebra to show that the space of inequivalent open string field theories is isomorphic to the space of classical closed string backgrounds. As a further application of the open-closed homotopy algebra, we show that string field theory is background independent and locally unique in a very precise sense. Finally, we discuss topological string theory in the framework of homotopy algebras and find a generalized correspondence between closed strings and open string field theories.     

光互连Omega网络与全交叉网络拓扑等价的多样性

本文对互连网络拓朴等价的分析方法作了简单评述,并采用互连网络拓朴等价的图分析法分析了自由空间光学互连Omega网络与全交叉网络的拓朴等价及其多样性,拓展了Omega网络在通信交换、数字光计算以及并行多处理机系统的潜在应用。     

Topological Classification of the Magnetization States in the Hole-Including Ferromagnets

In this paper the problem of topological classification of the magnetization states in the hole-including ferromagnets is comprehensively studied. The main result is that the set of homotopy classes of magnetization states, in a ferromagnet including a family of noninteracting holes of cylinder, sphere and annulus types with numbers m, k and l, respectively, can be constructed into a group isomorphic to z^k+l, the (k + l)-dimensional discrete vector group.     

同伦群理论在液晶缺陷中的应用

本文介绍了液晶缺陷研究的进展,并用同伦群理论讨论了各种类型液晶中不同维数的缺陷的分类,还简单讨论了液晶中缺陷强度所遵循的拓扑性质。     

含有长程拓扑性无序螺位错晶格中因势场引起的散射态和束缚态

螺位错的长程拓扑性无序对固体中所传播的波提供特殊的介体。用这种介体研究电势对电子态的影响。作为简单的例子要使用方势阱模型。在这种介体中用相移分析法能成功地得到散射解。未微扰的波函数不是平面波而是Aharouov-Bohm方程的严格解。束缚态能级的数目和位置依赖于电子的耦合和拓扑性无序。     

THE STUDY OF TOPOLOGICAL TERMS OF THE NONLINEAR SIGMA MODEL

The canonical system of O(3) nonlinear sigma model in 1+1 dimensions is studied in this paper.It is shown that the topological term in the model will disappear under a suitable canonical transformation for the system.The significance of this result is discussed.     

Majorana bound state of a Bogoliubov-de Gennes-Dirac Hamiltonian in arbitrary dimensions

We study a Majorana zero-energy state bound to a hedgehog-like point defect in a topological superconductor described by a Bogoliubov-de Gennes (BdG)-Dirac type effective Hamiltonian. We first give an explicit wave function of a Majorana state by solving the BdG equation directly, from which an analytical index can be obtained. Next, by calculating the corresponding topological index, we show a precise equivalence between both indices to confirm the index theorem. Finally, we apply this observation to reexamine the role of another topological invariant, i.e., the Chern number associated with the Berry curvature proposed in the study of protected zero modes along the lines of topological classification of insulators and superconductors. We show that the Chern number is equivalent to the topological index, implying that it indeed reflects the number of zero-energy states. Our theoretical model belongs to the BDI class from the viewpoint of symmetry, whereas the spatial dimension d of the system is left arbitrary throughout the paper.     

逆轨道分析法确定一维映象的拓扑熵

本文推广了文献[1]的工作,并用逆轨道分析法说明了本文所列公式的证明。据此可以算出整个参数区间中任一点上的拓扑熵值。在讨论“*”乘对拓扑熵值影响的基础上得到了一维映象拓扑熵的整体印象。 关键词：     

光互连Omega网络与榕树网络拓扑等价的多样性

本文对互连网络拓扑等介的分析方法作了综合评述。采用图分析法研究了光互连Ｏｍｅｇａ网络与榕树网络拓扑等价的多样性，得到了Ｏｍｅｇａ网络与榕树网络具有拓扑等价性质的多套逻辑名结构。     

一维单峰映象的拓扑熵

在对Logistic映象数值计算的基础上,我们分析了一维单峰映象的逆轨道结构,证明了不同参数处逆轨道总数N(n)随求逆次数n而变化的递推公式。借此解析地求得了在倍周期区中h(f)≡0;在U序列RLR²¹的m=3+2l周期点上h(f)=logα_mp,其中α_mp为方程α^m-2α^m-2-1=0的最大实根;在2^j-1常和2j带交界处h_j(f)=(1/2)^jlog2,由此可得聚点μ_∞处拓扑熵的标度指数t=0.449806…。在此基础上,我们还求得了混沌区的周期窗口,U序列RL^aR^b所对应的各点处的拓扑熵,以及h_R*Q(f)=(1/2)h_Q(f)的关系。证明是在M.S.S.规则和“*”乘法则的基础上进行的。所以本文的结果对一维单峰映象是普适的。 关键词：     

Changing topology and nontrivial homotopy

A method is proposed for extending the path integral to a sum over paths which change topology. This is used to show that topological contributions to a field theory path integral arising from nontrivial homotopy on the background space are completely determined in the free theory. The method is applied to extend (“third quantize”) field theory to backgrounds which change topology (e.g. string theory) and to show that topological contributions from nontrivial homotopy of field histories in the target space are completely determined by the field theory on a fixed background.     

有序介质中缺陷的拓扑理论

本文评述介绍了有序介质中缺陷的拓扑理论,着重于表述同伦论的数学框架并讨论了几个理想的可解的例。     

Topological hierarchy matters — topological matters with superlattices of defects

Topological insulators/superconductors are new states of quantum matter with metallic edge/surface states.In this paper,we review the defects effect in these topological states and study new types of topological matters — topological hierarchy matters.We find that both topological defects(quantized vortices) and non topological defects(vacancies) can induce topological mid-gap states in the topological hierarchy matters after considering the superlattice of defects.These topological mid-gap states have nontrivial topological properties,including the nonzero Chern number and the gapless edge states.Effective tight-binding models are obtained to describe the topological mid-gap states in the topological hierarchy matters.     

规范理论中反常的拓扑意义与规范群的?ech-de Rham上同调

本文分析了规范群上同调的拓扑障碍。指出规范群上同调的上边缘算子相当于?ech的差映射算子。采用逐级分区的方法克服以往常用的d^-1算子的含混性,而且将各阶上闭链与指数Z相联系,澄清了规范群上闭链的整体拓扑意义。 关键词：     

Some aspects of the theory of defects of ordered media and gauge fields related to foliations

When translational symmetry is broken in the ground state, the homotopy theory of defects of ordered media has to be supplemented with integrability conditions, coming from the theory of foliations. These show how some homotopy classes split into several distinct defects, while other homotopy classes do not occur physically. This framework can also be used in order to discuss defects of gauge fields, where in a first approximation classifying spaces play the role of the manifolds of internal states.     

Topological and affine classification of complete noncompact flat 4-manifolds

In this paper we give topological and affine classification of complete noncompact flat 4-manifolds. In particular, we show that the number of diffeomorphism classes of them is equal to 44. The affine classification uses the results of [M. Sadowski, Affinely equivalent complete flat manifolds, Cent. Eur. J. Math. 2 (2) (2004) 332–338]. The affine and the topological equivalence classes are the same for flat manifolds not homotopy equivalent to S¹,T²$S^1,T^2$ or the Klein bottle.     

循环量子系统中状态演化的Bloch定理和同步几何相位的统一

对于Hamiltonian随时间作周期变化的量子系统中状态的演化，Bloch定理亦成立，并可据此定义一种新的几何相位———Bloch相位．证明用这种新的几何相位可以把迄今发现的所有同步（即量子态演化一周后获得的）几何相位统一起来，即Bloch相位等于Pancharatnam相位、Aharonov-Anandan相位和Lewis-Riesenfeld相位，并且在绝热条件下化为Bery相位．为此，先对Pancharatnam相位、Aharonov-Anandan相位和Lewis-Riesenfeld相位的定义作等价的改变，使它们变得有物理意义，并把Lewis-Riesenfeld相位和Berry相位推广到简并情形．还讨论了Bloch相位的求解问题 关键词：