Vortices for the magnetic Ginzburg-Landau theory in curved space
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916595078529024 |
|---|---|
| author | Cao, Lei Xu, Yilu Chen, Shouxin |
| author_facet | Cao, Lei Xu, Yilu Chen, Shouxin |
| contents | Since the Ginzburg-Landau theory is concerned with macroscopic phenomena, and gravity affects how objects interact at the macroscopic level. It becomes relevant to study the Ginzburg-Landau theory in curved space, that is, in the presence of gravity. In this paper, some existence theorems are established for the vortex solutions of the magnetic Ginzburg-Landau theory coupled to the Einstein equations. First, when the coupling constant λ=1, we get a self-dual structure from the Ginzburg-Landau theory, then a partial differential equation with a gravitational term that has power-type singularities is deduced from the coupled system. To overcome the difficulty arising from the orders of singularities at the vortices, a constraint minimization method and a monotone iteration method are employed. We also show that the quantized flux and total curvature are determined by the number of vortices. Second, when the coupling constant λ>0, we use a suitable ansatz to get the radially symmetric case for the magnetic Ginzburg-Landau theory in curved space. The existence of the symmetric vortex solutions are obtained through combining a two-step iterative shooting argument and a fixed-point theorem approach. Some fundamental properties of the solutions are established via applying a series of analysis techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01151 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Vortices for the magnetic Ginzburg-Landau theory in curved space Cao, Lei Xu, Yilu Chen, Shouxin Mathematical Physics 35J57, 35Q75, 81T10 Since the Ginzburg-Landau theory is concerned with macroscopic phenomena, and gravity affects how objects interact at the macroscopic level. It becomes relevant to study the Ginzburg-Landau theory in curved space, that is, in the presence of gravity. In this paper, some existence theorems are established for the vortex solutions of the magnetic Ginzburg-Landau theory coupled to the Einstein equations. First, when the coupling constant λ=1, we get a self-dual structure from the Ginzburg-Landau theory, then a partial differential equation with a gravitational term that has power-type singularities is deduced from the coupled system. To overcome the difficulty arising from the orders of singularities at the vortices, a constraint minimization method and a monotone iteration method are employed. We also show that the quantized flux and total curvature are determined by the number of vortices. Second, when the coupling constant λ>0, we use a suitable ansatz to get the radially symmetric case for the magnetic Ginzburg-Landau theory in curved space. The existence of the symmetric vortex solutions are obtained through combining a two-step iterative shooting argument and a fixed-point theorem approach. Some fundamental properties of the solutions are established via applying a series of analysis techniques. |
| title | Vortices for the magnetic Ginzburg-Landau theory in curved space |
| topic | Mathematical Physics 35J57, 35Q75, 81T10 |
| url | https://arxiv.org/abs/2502.01151 |