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A quantization property for static Ginzburg-Landau vortices

✍ Scribed by Fang-Hua Lin; Tristan Rivière

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
130 KB
Volume
54
Category
Article
ISSN
0010-3640

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✦ Synopsis

For any critical point of the complex Ginzburg-Landau functional in dimension 3, we prove that, for large coupling constants, κ = 1 ε ; if the energy of this critical point on a ball of a given radius r is relatively small compared to r log r ε , then the ball of half-radius contains no vortex (the modulus of the solution is larger than 1 2 ). We then show how this property can be applied to describe limiting vortices as ε → 0.

📜 SIMILAR VOLUMES

Lines of vortices for solutions of the G
Lines of vortices for solutions of the Ginzburg–Landau equations
✍ Hassen Aydi 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 255 KB

For disc domains and for periodic models, we construct solutions of the Ginzburg-Landau equations which verify in the limit of a large Ginzburg-Landau parameter specified qualitative properties: the limit density of the vortices concentrates on lines.