RELATIONS BETWEEN DEFECTS IN THE BULK AND ON THE SURFACE OF AN ORDERED MEDIUM - A TOPOLOGICAL INVESTIGATION

被引:6
作者
TREBIN, HR
KUTKA, R
机构
[1] ISAAC NEWTON INST MATH SCI, CAMBRIDGE, ENGLAND
[2] SIEMENS AG, ZENTRALABT FORSCH & ENTWICKLUNG, D-81739 MUNICH, GERMANY
来源
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 1995年 / 28卷 / 07期
关键词
D O I
10.1088/0305-4470/28/7/020
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Starting from a proposal of Volovik we investigate surface point, line, and wall defects with the aid of relative homotopy groups. The exact sequence of homotopy groups is used in interpreting the relations between surface and bulk singularities. In particular, we consider the possibilities for surface singularities to move into the bulk, for bulk singularities to leave the medium through the surface, and for singular loops to be broken apart by the surface. The theory is extended to the case where the surface induces a thermodynamic phase differing from that in the bulk. An example is given of a biaxial nematic surface with the Klein bottle as the order-parameter space. Due to the fundamental theorem for homotopy groups of fibre bundles, the classification scheme of surface defects is identical for all pairs of bulk and surface order-parameter spaces which are related by an inverse-bundle projection.
引用
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页码:2005 / 2014
页数:10
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