Introduction to superconductivity and self-duality as a cooperation mechanism to complexity emergence
Autor(a) principal: | |
---|---|
Data de Publicação: | 2022 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFPE |
Texto Completo: | https://repositorio.ufpe.br/handle/123456789/45249 |
Resumo: | Initially we conduct a review of superconductivity and examine a variety of topics, includ- ing the Fermi-Landau theory, the generic Landau theory of phase transition with a focus on Ginzburg-Landau, the Fhrölich model, Bardeen-Cooper-Schrieffer, and Bogoliubov theories, as well as their relation to the coherent Glauber states. Next, we establish the connection between microscopic theories and GL, a result pioneered by Gor’kov, and recent developments in the Extended Ginzburg-Landau theory by A.Shanenko and A.Vagov et al. - a step beyond Gor’kov, providing a self-consistent expansion valid further away from the critical temperature. These results are reproduced by formulating an alternative time-saving method for computing higher-order Landau theories of superfluid phase transition (in the absence of the induction- field coupling). This is accomplished through the formulation of a diagrammatic dictionary and a concise collection of rules. The primary original contribution of this work, though, is the description of novel semi-analytic solutions to the self-dual superconducting solutions at the Bogomol’nyi point (κ = 1/√2) and their correspondence to the appearance of patterns similar to those in U.Krägeloh’s (1969) pioneering measurement in "Flux line lattices in the intermediate state of superconductors near κ = 1/√2". The semi-analytic solutions are coined stripe, bubble and donut. They exhibit stable thermodynamics beyond κ = 1/√2, in the ‘intertype’ domain, as we predict from the Extended Ginzburg Landau theory. We observe the results in the time-dependent Ginzburg-Landau model starting from configurations similar to the semi-analytic solutions as ab initio ansatz. The time-evolved solutions qualitatively co- incide with Krägeloh’s experimental results. The obtained results allow us to cast doubt on a widely accepted view of how complexity develops. We present a phenomenology in which ’cooperation’ rather than ’competition’ is the appropriate keyword for justifying the complexity emergence. |
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SARMENTO, Matheus de Araújohttp://lattes.cnpq.br/7950752191342432http://lattes.cnpq.br/4321118621178584RAPOSO, Ernesto Carneiro Pessoa2022-07-27T15:46:06Z2022-07-27T15:46:06Z2022-03-23SARMENTO, Matheus de Araújo. Introduction to superconductivity and self-duality as a cooperation mechanism to complexity emergence. 2022. Dissertação (Mestrado em Física) - Universidade Federal de Pernambuco, Recife, 2022.https://repositorio.ufpe.br/handle/123456789/45249Initially we conduct a review of superconductivity and examine a variety of topics, includ- ing the Fermi-Landau theory, the generic Landau theory of phase transition with a focus on Ginzburg-Landau, the Fhrölich model, Bardeen-Cooper-Schrieffer, and Bogoliubov theories, as well as their relation to the coherent Glauber states. Next, we establish the connection between microscopic theories and GL, a result pioneered by Gor’kov, and recent developments in the Extended Ginzburg-Landau theory by A.Shanenko and A.Vagov et al. - a step beyond Gor’kov, providing a self-consistent expansion valid further away from the critical temperature. These results are reproduced by formulating an alternative time-saving method for computing higher-order Landau theories of superfluid phase transition (in the absence of the induction- field coupling). This is accomplished through the formulation of a diagrammatic dictionary and a concise collection of rules. The primary original contribution of this work, though, is the description of novel semi-analytic solutions to the self-dual superconducting solutions at the Bogomol’nyi point (κ = 1/√2) and their correspondence to the appearance of patterns similar to those in U.Krägeloh’s (1969) pioneering measurement in "Flux line lattices in the intermediate state of superconductors near κ = 1/√2". The semi-analytic solutions are coined stripe, bubble and donut. They exhibit stable thermodynamics beyond κ = 1/√2, in the ‘intertype’ domain, as we predict from the Extended Ginzburg Landau theory. We observe the results in the time-dependent Ginzburg-Landau model starting from configurations similar to the semi-analytic solutions as ab initio ansatz. The time-evolved solutions qualitatively co- incide with Krägeloh’s experimental results. The obtained results allow us to cast doubt on a widely accepted view of how complexity develops. We present a phenomenology in which ’cooperation’ rather than ’competition’ is the appropriate keyword for justifying the complexity emergence.Inicialmente conduzimos uma revisão da supercondutividade e examinamos uma variedade de tópicos, incluindo a teoria de Fermi-Landau, a teoria genérica de Landau de transição de fase com foco em Ginzburg-Landau, o modelo Fhrölich, as teorias de Bardeen-Cooper-Schrieffer e Bogoliubov e sua relação com os estados coerentes de Glauber. Em seguida, estabelecemos a conexão entre teorias microscópicas e GL, resultado pioneiro de Gor’kov, e desenvolvimen- tos recentes na teoria Extended Ginzburg-Landau (EGL) por A.Shanenko e A.Vagov et al. - um passo além de Gor’kov, fornecendo uma expansão auto-consistente válida mais longe da temperatura crítica. O resultado é reproduzido pela formulação de um método eficiente para calcular teorias de Landau de ordem mais alta para transição de fase superfluida (na ausência do acoplamento de campo de indução). Isso é realizado pela construção de um dicionário di- agramático e uma coleção concisa de regras. A principal contribuição original deste trabalho, no entanto, é a descrição de novas soluções semi-analíticas para as soluções supercondutoras auto-duais no ponto Bogomol’nyi (κ = 1/√2) e sua correspondência com o aparecimento de padrões semelhantes aos da medição pioneira de U.Krägeloh (1967) em "Flux line lattices in the middle state of superconductors near κ = 1/√2". As soluções semi-analíticas são denomi-nadas listra, bolha e rosca. Elas exibem termodinâmica estável além de κ = 1/√2, no domínio ’intertype’, como prevemos a partir da teoria Extended Ginzburg Landau. As simulações no modelo de Ginzburg-Landau dependente do tempo são executadas a partir de configurações semelhantes às soluções semi-analíticas como ab initio ansatz, a solução evoluída no tempo coincide qualitativamente com os resultados experimentais de Krägeloh. Os resultados obtidos permitem questionar uma visão amplamente aceita de como a complexidade se desenvolve. Apresentamos uma fenomenologia em que ’colaboração’ ao invés de ’competição’ é a palavra- chave mais adequada para justificar o surgimento da complexidade.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em FisicaUFPEBrasilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/embargoedAccessFísica teórica e computacionalSuperconductividadeIntroduction to superconductivity and self-duality as a cooperation mechanism to complexity emergenceinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesismestradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPECC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufpe.br/bitstream/123456789/45249/2/license_rdfe39d27027a6cc9cb039ad269a5db8e34MD52ORIGINALDISSERTAÇÃO Matheus de Araújo Sarmento.pdfDISSERTAÇÃO Matheus de Araújo Sarmento.pdfapplication/pdf13929098https://repositorio.ufpe.br/bitstream/123456789/45249/1/DISSERTA%c3%87%c3%83O%20Matheus%20de%20Ara%c3%bajo%20Sarmento.pdf991ff38b7017390775d59a737d8f794fMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-82142https://repositorio.ufpe.br/bitstream/123456789/45249/3/license.txt6928b9260b07fb2755249a5ca9903395MD53TEXTDISSERTAÇÃO Matheus de Araújo Sarmento.pdf.txtDISSERTAÇÃO Matheus de Araújo Sarmento.pdf.txtExtracted texttext/plain291825https://repositorio.ufpe.br/bitstream/123456789/45249/4/DISSERTA%c3%87%c3%83O%20Matheus%20de%20Ara%c3%bajo%20Sarmento.pdf.txte87bca7d125ff55bb363af14fa9d6e44MD54THUMBNAILDISSERTAÇÃO Matheus de Araújo Sarmento.pdf.jpgDISSERTAÇÃO Matheus de Araújo Sarmento.pdf.jpgGenerated Thumbnailimage/jpeg1249https://repositorio.ufpe.br/bitstream/123456789/45249/5/DISSERTA%c3%87%c3%83O%20Matheus%20de%20Ara%c3%bajo%20Sarmento.pdf.jpgb51e4da7eee4ae1e4c5d9cbf2b1faa9dMD55123456789/452492022-07-28 02:49:12.176oai:repositorio.ufpe.br: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ório InstitucionalPUBhttps://repositorio.ufpe.br/oai/requestattena@ufpe.bropendoar:22212022-07-28T05:49:12Repositório Institucional da UFPE - Universidade Federal de Pernambuco (UFPE)false |
dc.title.pt_BR.fl_str_mv |
Introduction to superconductivity and self-duality as a cooperation mechanism to complexity emergence |
title |
Introduction to superconductivity and self-duality as a cooperation mechanism to complexity emergence |
spellingShingle |
Introduction to superconductivity and self-duality as a cooperation mechanism to complexity emergence SARMENTO, Matheus de Araújo Física teórica e computacional Superconductividade |
title_short |
Introduction to superconductivity and self-duality as a cooperation mechanism to complexity emergence |
title_full |
Introduction to superconductivity and self-duality as a cooperation mechanism to complexity emergence |
title_fullStr |
Introduction to superconductivity and self-duality as a cooperation mechanism to complexity emergence |
title_full_unstemmed |
Introduction to superconductivity and self-duality as a cooperation mechanism to complexity emergence |
title_sort |
Introduction to superconductivity and self-duality as a cooperation mechanism to complexity emergence |
author |
SARMENTO, Matheus de Araújo |
author_facet |
SARMENTO, Matheus de Araújo |
author_role |
author |
dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/7950752191342432 |
dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/4321118621178584 |
dc.contributor.author.fl_str_mv |
SARMENTO, Matheus de Araújo |
dc.contributor.advisor1.fl_str_mv |
RAPOSO, Ernesto Carneiro Pessoa |
contributor_str_mv |
RAPOSO, Ernesto Carneiro Pessoa |
dc.subject.por.fl_str_mv |
Física teórica e computacional Superconductividade |
topic |
Física teórica e computacional Superconductividade |
description |
Initially we conduct a review of superconductivity and examine a variety of topics, includ- ing the Fermi-Landau theory, the generic Landau theory of phase transition with a focus on Ginzburg-Landau, the Fhrölich model, Bardeen-Cooper-Schrieffer, and Bogoliubov theories, as well as their relation to the coherent Glauber states. Next, we establish the connection between microscopic theories and GL, a result pioneered by Gor’kov, and recent developments in the Extended Ginzburg-Landau theory by A.Shanenko and A.Vagov et al. - a step beyond Gor’kov, providing a self-consistent expansion valid further away from the critical temperature. These results are reproduced by formulating an alternative time-saving method for computing higher-order Landau theories of superfluid phase transition (in the absence of the induction- field coupling). This is accomplished through the formulation of a diagrammatic dictionary and a concise collection of rules. The primary original contribution of this work, though, is the description of novel semi-analytic solutions to the self-dual superconducting solutions at the Bogomol’nyi point (κ = 1/√2) and their correspondence to the appearance of patterns similar to those in U.Krägeloh’s (1969) pioneering measurement in "Flux line lattices in the intermediate state of superconductors near κ = 1/√2". The semi-analytic solutions are coined stripe, bubble and donut. They exhibit stable thermodynamics beyond κ = 1/√2, in the ‘intertype’ domain, as we predict from the Extended Ginzburg Landau theory. We observe the results in the time-dependent Ginzburg-Landau model starting from configurations similar to the semi-analytic solutions as ab initio ansatz. The time-evolved solutions qualitatively co- incide with Krägeloh’s experimental results. The obtained results allow us to cast doubt on a widely accepted view of how complexity develops. We present a phenomenology in which ’cooperation’ rather than ’competition’ is the appropriate keyword for justifying the complexity emergence. |
publishDate |
2022 |
dc.date.accessioned.fl_str_mv |
2022-07-27T15:46:06Z |
dc.date.available.fl_str_mv |
2022-07-27T15:46:06Z |
dc.date.issued.fl_str_mv |
2022-03-23 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
SARMENTO, Matheus de Araújo. Introduction to superconductivity and self-duality as a cooperation mechanism to complexity emergence. 2022. Dissertação (Mestrado em Física) - Universidade Federal de Pernambuco, Recife, 2022. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufpe.br/handle/123456789/45249 |
identifier_str_mv |
SARMENTO, Matheus de Araújo. Introduction to superconductivity and self-duality as a cooperation mechanism to complexity emergence. 2022. Dissertação (Mestrado em Física) - Universidade Federal de Pernambuco, Recife, 2022. |
url |
https://repositorio.ufpe.br/handle/123456789/45249 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
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http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
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embargoedAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
dc.publisher.program.fl_str_mv |
Programa de Pos Graduacao em Fisica |
dc.publisher.initials.fl_str_mv |
UFPE |
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Brasil |
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Universidade Federal de Pernambuco |
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