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Topological aspect of vortex lines in two-dimensional Gross–Pitaevskii theory |
| Zhao Li (赵力)a, Yang Jie (杨捷)a, Xie Qun-Ying (谢群英)a b, Tian Miao (田苗)c |
a Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China;
b School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China;
c School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730000, China |
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Abstract Using the φ-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 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 φ-mapping topological current theory also provides a reasonable way to study the bifurcation theory of vortex lines in the two-dimensional Gross-Pitaevskii theory.
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Received: 25 August 2011
Revised: 14 April 2012
Accepted manuscript online:
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PACS:
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03.75.Lm
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(Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)
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47.32.C-
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(Vortex dynamics)
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02.40.Pc
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(General topology)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10905026 and 10905027) and the Program of Science and Technology Development of Lanzhou, China (Grant No. 2010-1-129). |
Corresponding Authors:
Zhao Li
E-mail: lizhao@lzu.edu.cn
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Cite this article:
Zhao Li (赵力), Yang Jie (杨捷), Xie Qun-Ying (谢群英), Tian Miao (田苗) Topological aspect of vortex lines in two-dimensional Gross–Pitaevskii theory 2012 Chin. Phys. B 21 090304
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