Topological aspect of vortex lines in two-dimensional Gross-Pitaevskii theory

被引：0

作者：

赵力 ^{[1
]}

杨捷 ^{[1
]}

谢群英 ^{[1
,2
]}

田苗 ^{[3
]}

机构：

[1] Institute of Theoretical Physics, Lanzhou University

[2] School of Information Science and Engineering, Lanzhou University

[3] School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University

来源：

Chinese Physics B | 2012年 / 21卷 / 09期

关键词：

Gross-Pitaevskii equation; Bose-Einstein condensate; vortex line; bifurcation theory;

D O I：

暂无

中图分类号：

O413.1 [量子力学（波动力学、矩阵力学）]; O189 [拓扑（形势几何学）];

学科分类号：

070205 ; 0809 ; 070104 ;

摘要：

Using the -mapping topological theory, we study the topological structure of vortex lines in a two-dimensional generalized Gross-Pitaevskii theory in (3+1)-dimensional space-time. We obtain the reduced dynamic equation in the framework of the two-dimensional Gross-Pitaevskii theory, from which a conserved dynamic quantity is derived on the stable vortex lines. Such equations can also be used to discuss Bose-Einstein condensates in heterogeneous and highly nonlinear systems. We obtain an exact dynamic equation with a topological term, which is ignored in traditional hydrodynamic equations. The explicit expression of vorticity as a function of the order parameter is derived, where the δ function indicates that the vortices can only be generated from the zero points of Φ and are quantized in terms of the Hopf indices and Brouwer degrees. The -mapping topological current theory also provides a reasonable way to study the bifurcation theory of vortex lines in the two-dimensional Gross-Pitaevskii theory.

引用

页码：94 / 102

页数：9