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非相对论Chern-Simons多涡旋解的拓扑结构(英文)

Topological Structure of Nonrelativistic ChernSimons Vortices Solution

    摘要
  • 摘要: 运用规范势分解理论研究了JackiwPi模型中的自对偶方程, 得到一个新的自对偶方程， 发现了ChernSimons多涡旋解与拓扑荷之间的联系。为了研究JackiwPi模型多涡旋解的拓扑性质， 构造了一个新的静态自对偶ChernSimons多涡旋解,每个涡旋由5个实参数描述。 2个实参量用来描述涡旋的位置， 2个实参量用来描述涡旋的尺度和相位, 还有一个实参量描述涡旋的荷。 为了研究拓扑数对涡旋形状的影响， 给出了具有不同拓扑数的多涡旋解。 另外还研究了该涡旋解的磁通量的拓扑量子化。

     

    Abstract: By using the gauge potential decomposition, we have discussed the selfdual equation and its solution in JackiwPi model. We obtained a new concrete selfdual equation and find relationship between ChernSimons vortex solution and topological number which is determined by Hopf indices and Brouwer degrees of mapping. To show the meaning of topological number we presented several figures with different topological numbers. In order to investigate the topological properties of many vortices, 5 parameters (two positions, one scale, one phase per vortex and one charge of each vortex) have been used to describe each vortex in many vortices solution in JackiwPi model. For many vortices, three figures with different topological numbers have been drown to show the effect of the charge on the many vortices solution. We also studied the quantization of flux of those vortices related to the topological numbers in this case.

     

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