The Bifurcation of Topological Current in the O(n) Symmetrical Time-Dependent Ginzburg-Landau Model

Abstract

Using the method of φ-mapping topological current theory, the bifurcation behavior of the topological current in the O(n) symmetrical TDGL model at the critical points of the order parameter field is investigated in detail. The different directions of the branch curves at the critical points are obtained. The topology properties of physical systems play important roles in studying many physical problems. The φ-mapping topological current theory provides a powerful frameworkto describe the topological invariants and structure of physical systems. 1),2) Recently, much workhas been done on the time-dependent Ginzburg-Landau (TDGL) model. 3) - 6) Using the method of φ-mapping, we have studied the inner structure of the topological current, and classified the topological defects with Brouwer degrees and Hopf indices of the φ-mapping. 1) In this paper, we use the φ-mapping topological current theory to study the bifurcation behavior of vortex current in the TDGL model for a nonconserved n-component order parameter. The TDGL model for a nonconserved n-component order parameter �(x, t )= [φ 1 (x, t), ··· ,φ n (x, t)] is governed by the Langevin equation