Singular GinzburgLandau Vortices
(1998) Abstract
 In this thesis we study the critical GinzburgLandau 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 GinzburgLandau 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:
https://lup.lub.lu.se/record/18782
 author
 Aigner, Mats ^{LU}
 supervisor
 opponent

 Sadun, Lorenzo
 organization
 publishing date
 1998
 type
 Thesis
 publication status
 published
 subject
 keywords
 Mathematics, singularities, GinzburgLandau, vortices, Matematik
 pages
 81 pages
 publisher
 Mathematics (Faculty of Sciences)
 defense location
 Matematiska Institutionen, sal C
 defense date
 19980522 10:15:00
 external identifiers

 other:ISRN: LUNFD6/NFMA98/1008SE
 ISBN
 9162830155
 language
 English
 LU publication?
 yes
 id
 ccc1e09245c848e2bc7acaebcbde10c2 (old id 18782)
 date added to LUP
 20160401 16:05:56
 date last changed
 20181121 20:38:42
@phdthesis{ccc1e09245c848e2bc7acaebcbde10c2, abstract = {{In this thesis we study the critical GinzburgLandau 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 = {{9162830155}}, keywords = {{Mathematics; singularities; GinzburgLandau; vortices; Matematik}}, language = {{eng}}, publisher = {{Mathematics (Faculty of Sciences)}}, school = {{Lund University}}, title = {{Singular GinzburgLandau Vortices}}, year = {{1998}}, }