Self-Dual Vortices in the Fractional Quantum Hall System

Details Self-Dual Vortices in the Fractional Quantum Hall System Self-Dual Vortices in the Fractional Quantum Hall System

2007-12-24

arxiv.org/abs/0712.3961v1

Int.J.Mod.Phys.B00:1-11,2009

Physics

High Energy Physics

High Energy Physics - Theory

13 pages 10 figures. accepted by IJMPB

Scientific paper

10.1142/S0217979209052480

Based on the $\phi$-mapping theory, we obtain an exact Bogomol'nyi self-dual equation with a topological term, which is ignored in traditional self-dual equation, in the fractional quantum Hall system. It is revealed that there exist self-dual vortices in the system. We investigate the inner topological structure of the self-dual vortices and show that the topological charges of the vortices are quantized by Hopf indices and Brouwer degrees. Furthermore, we study the branch processes in detail. The vortices are found generating or annihilating at the limit points and encountering, splitting or merging at the bifurcation points of the vector field $\vec\phi$.

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