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Singular Ginzburg-Landau Vortices

Aigner, Mats LU (1998)
Abstract
In this thesis we study the critical Ginzburg-Landau action, defined on fields in the plane which are allowed to have a finite number of singularities. We show that a topological invariant, the degree, can be defined under the assumption of finite action only. The action is bounded below by a constant times the degree, and the fields which realize this lower bound satisfy a first order differential equation. The critical points of the action satisfy a second order differential equation.



Using methods of C. Taubes, we give a classification of all finite action solutions to the first order equation, and we show that if there is at most one singularity, then the first and second order equations are equivalent. By different... (More)
In this thesis we study the critical Ginzburg-Landau action, defined on fields in the plane which are allowed to have a finite number of singularities. We show that a topological invariant, the degree, can be defined under the assumption of finite action only. The action is bounded below by a constant times the degree, and the fields which realize this lower bound satisfy a first order differential equation. The critical points of the action satisfy a second order differential equation.



Using methods of C. Taubes, we give a classification of all finite action solutions to the first order equation, and we show that if there is at most one singularity, then the first and second order equations are equivalent. By different methods we then construct solutions to the second order equation with more than one singularity which does not solve the first order equation. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Sadun, Lorenzo
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Mathematics, singularities, Ginzburg-Landau, vortices, Matematik
pages
81 pages
publisher
Mathematics (Faculty of Sciences)
defense location
Matematiska Institutionen, sal C
defense date
1998-05-22 10:15:00
external identifiers
  • other:ISRN: LUNFD6/NFMA-98/1008-SE
ISBN
91-628-3015-5
language
English
LU publication?
yes
id
ccc1e092-45c8-48e2-bc7a-caebcbde10c2 (old id 18782)
date added to LUP
2016-04-01 16:05:56
date last changed
2018-11-21 20:38:42
@phdthesis{ccc1e092-45c8-48e2-bc7a-caebcbde10c2,
  abstract     = {{In this thesis we study the critical Ginzburg-Landau action, defined on fields in the plane which are allowed to have a finite number of singularities. We show that a topological invariant, the degree, can be defined under the assumption of finite action only. The action is bounded below by a constant times the degree, and the fields which realize this lower bound satisfy a first order differential equation. The critical points of the action satisfy a second order differential equation.<br/><br>
<br/><br>
Using methods of C. Taubes, we give a classification of all finite action solutions to the first order equation, and we show that if there is at most one singularity, then the first and second order equations are equivalent. By different methods we then construct solutions to the second order equation with more than one singularity which does not solve the first order equation.}},
  author       = {{Aigner, Mats}},
  isbn         = {{91-628-3015-5}},
  keywords     = {{Mathematics; singularities; Ginzburg-Landau; vortices; Matematik}},
  language     = {{eng}},
  publisher    = {{Mathematics (Faculty of Sciences)}},
  school       = {{Lund University}},
  title        = {{Singular Ginzburg-Landau Vortices}},
  year         = {{1998}},
}