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arXiv · 2111.06600

Existence of global vortices in a class of Ginzburg-Landau models

Xiaosen Han·Kexin Zhang
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Abstract

In this paper, the two-component Ginzburg-Landau (TCGL) model, which is an important research object in mathematics and physics of two scalar fields with $U(1)\times U(1)$ symmetry, is studied in detail by the shooting method and the fixed point theorem, which contains two cases: single vacuum expectation value (1VEV) and two vacuum expectation values (2VEV). This represents two different physical states: superconductivity-normal state and superconductivity superconductivity state, and we prove the existence, uniqueness, asymptotic properties and quantization of the solutions to these two boundary value problems.

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Xiaosen Han, Kexin Zhang. 2021-11-12. Existence of global vortices in a class of Ginzburg-Landau models. https://arxiv.org/abs/2111.06600

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