拓扑空间(组)的同伦等价变换及有序介质状态的拓扑分类

凝聚态和相变物理的一个重要部分是研究有序相的状态和缺陷,近二十年来,应用代数拓扑学方法对有序介质的状态和缺陷进行分类,增进了人们对相变等过程的认识,从而引起广泛的注意,虽然从本质上说,缺陷拓扑分类也可纳入状态拓扑分类的框架,国际上迄今的有关研究却主要针对缺陷;除织构(孤子)态外,对一般状态甚少涉及,本文试图     

在地心参照系中对地球赤道上落体偏东的计算

本文以突出落体偏东的物理图象为目的，在地心参照系中求出了地球赤道上落体偏东的大小，并指出现行理论力学教材中的结果是本文结果的近似情况。     

TOPOLOGICAL CLASSIFICATION OF 3D AND 2D SPIN STATES IN THE FERROMAGNETS CONTAINING ANNULUS- AND CYLINDER-TYPE CAVITIES

Methods of algebraic topology have been employed to classify ordinary (3D) and planar (2D) spin states in the ferromagnets containing annulus- and cylinder-type cavities. The main result of this paper is that the sets of homotopy classes of 3D and 2D spin states in a ferromagnet containing m non-winding up annulus-type cavities threaded by k cylinder-type cavities can be constructed into groups isomorphic to Z^m and Z^m+k, respectively. Here m,k = 0, 1, 2,…,Z^l denotes the l-dimensional discrete vector group.     

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：     

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：     

由含时边界条件的两种有限深量子势阱构造的哈密顿算符和它们的复BERRY相位

在量子基础理论的框架下分别从一维含时边界条件的半壁无限高量子势阱和三维含时边界条件的有限深球方势阱构造了两种描述带电粒子在电磁场作用下的新哈密顿算符.在绝热近似下，计算了这两种新量子体系的复Berry相位.     

TOPOLOGICAL CLASSIFICATION OF 3D AND 2D SPIN STATES IN A FERROMAGNET INCLUDING AN ANNULAR CAVITY

ＴＯＰＯＬＯＧＩＣＡＬＣＬＡＳＳＩＦＩＣＡＴＩＯＮＯＦ３ＤＡＮＤ２ＤＳＰＩＮＳＴＡＴＥＳＩＮＡＦＥＲＲＯＭＡＧＮＥＴＩＮＣＬＵＤＩＮＧＡＮＡＮＮＵＬＡＲＣＡＶＩＴＹ阎凤利，李伯臧￥ＹａｎＦｅｎｇｌｉ（Ｄｅｐｔ．ｏｆＰｈｙｓ，ＨｅｂｅｉＴｅａｃｈｅｒｓ...     

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：     

APPLYING THE HOMOTOPY EQUIVALENCE TRANSFORMATION OF TOPOLOGICAL SPACE SETS TO THE TOPOLOGICAL CLASSIFICATION OF STATES AND DEFECTS IN ORDERED MEDIA

In this paper the application of homotopy equivalence transformation (HET) of topological space sets to the topological classification of states and defects in ordered media is discussed. Firstly, an argument is pres-ented about the idea that for simplifying and even working out the classification and constructing homotopy class sets into groups, it is crucial to utilize the HET. As the theoretical basis for doing this we sum up the relevant results in homotopy theory into a theorem, called the "invariance theorem for HET". Secondly, in order to favor the utilization of this theorem, several propositions on homotopy equivalence between space sets are given. Finally, the absolute and relative topological dassification of states and defects is systemtically studied. The main results obtained are embodied in eight theorems.     

p=2U／3V系统的态函数形式

给出了压强ｐ、内能Ｕ和体积Ｖ满足ｐ＝２Ｕ／３Ｖ的系统的态函数形式。并据此讨论了理想 玻色气体、理想费米气体和通常的理想气体的状太民方程不同的热力学原因。