Zero modes and degrees of freedom of topological solitons on the plane

dc.contributor.advisorBarashenkov, I Ven_ZA
dc.contributor.authorAdams, Rory Montagueen_ZA
dc.date.accessioned2015-09-14T18:05:20Z
dc.date.available2015-09-14T18:05:20Z
dc.date.issued2003en_ZA
dc.descriptionIncludes bibliographical references.en_ZA
dc.description.abstractIn this thesis we analyse the coaxial multivortices of the Ginzburg-Landau, the Euclidean complex sine-Gordon-1 and -2 theories on the plane. More specifically, we determine the number of continuous free parameters describing the largest family of solutions, with these vortices as members. This is accomplished by obtaining the zero modes of the vortices. For the Ginzburg-Landau model we show that the multivortices do not belong to a larger family of solutions and only depend on parameters describing their global U(1) symmetry and translations in the plane. Thus it is not possible to continuously deform these coaxial multivortices into a system of multiple, separated vortices. In contrast, the multivortices of complex sine-Gordon-1 model are shown to have an infinite number of zero modes and can be continuously deformed into a configuration of multiple, separated vortices. We also show that the largest family of solutions, with these coaxial multivortices as members, is a recently discovered family describing non-coaxial multivortices. For the complex sine-Gordon-2, we show the coaxial multivortices belong to a larger family of solutions which depend on a finite number of continuous free parameters. We also speculate as to the form of solutions that this larger family can describe.en_ZA
dc.identifier.apacitationAdams, R. M. (2003). <i>Zero modes and degrees of freedom of topological solitons on the plane</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/13891en_ZA
dc.identifier.chicagocitationAdams, Rory Montague. <i>"Zero modes and degrees of freedom of topological solitons on the plane."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2003. http://hdl.handle.net/11427/13891en_ZA
dc.identifier.citationAdams, R. 2003. Zero modes and degrees of freedom of topological solitons on the plane. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Adams, Rory Montague AB - In this thesis we analyse the coaxial multivortices of the Ginzburg-Landau, the Euclidean complex sine-Gordon-1 and -2 theories on the plane. More specifically, we determine the number of continuous free parameters describing the largest family of solutions, with these vortices as members. This is accomplished by obtaining the zero modes of the vortices. For the Ginzburg-Landau model we show that the multivortices do not belong to a larger family of solutions and only depend on parameters describing their global U(1) symmetry and translations in the plane. Thus it is not possible to continuously deform these coaxial multivortices into a system of multiple, separated vortices. In contrast, the multivortices of complex sine-Gordon-1 model are shown to have an infinite number of zero modes and can be continuously deformed into a configuration of multiple, separated vortices. We also show that the largest family of solutions, with these coaxial multivortices as members, is a recently discovered family describing non-coaxial multivortices. For the complex sine-Gordon-2, we show the coaxial multivortices belong to a larger family of solutions which depend on a finite number of continuous free parameters. We also speculate as to the form of solutions that this larger family can describe. DA - 2003 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2003 T1 - Zero modes and degrees of freedom of topological solitons on the plane TI - Zero modes and degrees of freedom of topological solitons on the plane UR - http://hdl.handle.net/11427/13891 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/13891
dc.identifier.vancouvercitationAdams RM. Zero modes and degrees of freedom of topological solitons on the plane. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2003 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/13891en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematics and Applied Mathematicsen_ZA
dc.titleZero modes and degrees of freedom of topological solitons on the planeen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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