A new topological aspect in the O(n) symmetric time-dependent Ginzburg-Landau model

With the aid of phi-mapping topological current theory, the topological structure of vortices and the topological quantization of their topological charges in the TDGL model are obtained under the condition that the Jacobian D(phi/x) not equal 0. When D(phi/x) = 0, it is shown that there exists the crucial branch process case. Based on the implicit function theorem and the Taylor expansion, we detail the bifurcation of the vortex topological current and find different directions of the bifurcation. The vortices in the TDGL model are found to be multiply charged at the degenerate points of the order parameter field function phi. (C) 1999 Elsevier Science B.V.