Interactions between topological defects in (1+1) dimensions
Ano de defesa: | 2022 |
---|---|
Autor(a) principal: | |
Orientador(a): | |
Banca de defesa: | |
Tipo de documento: | Tese |
Tipo de acesso: | Acesso aberto |
Idioma: | por |
Instituição de defesa: |
Universidade Federal de Pernambuco
|
Programa de Pós-Graduação: |
Programa de Pos Graduacao em Fisica
|
Departamento: |
Não Informado pela instituição
|
País: |
Brasil
|
Palavras-chave em Português: | |
Link de acesso: | https://repositorio.ufpe.br/handle/123456789/44502 |
Resumo: | In this thesis, we study interactions between topological defects in two-dimensional spacetimes. These defects are called kinks. They are solutions of scalar field theories with localized energy which propagate without losing its shape. In order to understand the resonance phenomenon exhibited by those models, we built a toy model where the kink’s vibrational mode turns into a quasinormal mode. This causes the suppression of resonance windows and, consequently, its fractal structure is lost. Considering a higher order polynomial as the scalar field potential, we find kinks with long-range tails, which decay as a power law. We developed a numerical method to correctly initialize this systems and applied it to a scalar field model containing kinks with long-range tails in both sides. After the collision, the kink-antikink pair is annihilated for velocities below an ultra-relativistic critical velocity without bion formation. We also investigated a collision between wobbling kinks of the double sine-Gordon model. When the kinks are already wobbling before colliding, there appears resonance windows with separation after a single bounce. On the second half of the thesis, we focused on fermion-kink interactions. We studied what happens when a fermion binds to a wobbling kink. The result is that the fermion escapes from the kink as radiation and at a constant rate. This occurs if the energy gap between the initial state and the continuum threshold is not too large. Lastly, we investigated the interaction of a fermion with a background scalar field with an impurity that preserves half of the Bogomol’nyi–Prasad–Sommerfield (BPS) property. We found an adiabatic evolution near the BPS regime, which means that the system is at a static BPS solution at every moment. |
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CAMPOS, João Guilherme Ferreirahttp://lattes.cnpq.br/6341109305242477http://lattes.cnpq.br/4017443371706337MOHAMMADI, Azadeh2022-05-18T17:09:39Z2022-05-18T17:09:39Z2022-02-22CAMPOS, João Guilherme Ferreira. Interactions between topological defects in (1+1) dimensions. 2022. Tese (Doutorado em Física) - Universidade Federal de Pernambuco, Recife, 2022.https://repositorio.ufpe.br/handle/123456789/44502In this thesis, we study interactions between topological defects in two-dimensional spacetimes. These defects are called kinks. They are solutions of scalar field theories with localized energy which propagate without losing its shape. In order to understand the resonance phenomenon exhibited by those models, we built a toy model where the kink’s vibrational mode turns into a quasinormal mode. This causes the suppression of resonance windows and, consequently, its fractal structure is lost. Considering a higher order polynomial as the scalar field potential, we find kinks with long-range tails, which decay as a power law. We developed a numerical method to correctly initialize this systems and applied it to a scalar field model containing kinks with long-range tails in both sides. After the collision, the kink-antikink pair is annihilated for velocities below an ultra-relativistic critical velocity without bion formation. We also investigated a collision between wobbling kinks of the double sine-Gordon model. When the kinks are already wobbling before colliding, there appears resonance windows with separation after a single bounce. On the second half of the thesis, we focused on fermion-kink interactions. We studied what happens when a fermion binds to a wobbling kink. The result is that the fermion escapes from the kink as radiation and at a constant rate. This occurs if the energy gap between the initial state and the continuum threshold is not too large. Lastly, we investigated the interaction of a fermion with a background scalar field with an impurity that preserves half of the Bogomol’nyi–Prasad–Sommerfield (BPS) property. We found an adiabatic evolution near the BPS regime, which means that the system is at a static BPS solution at every moment.CNPqNesta tese, estudamos interações entre defeitos topológicos em uma dimensão espacial e uma temporal. Esses defeitos são chamados de kinks. Eles são soluções de teorias de campos escalares que possuem energia localizada e se propagam sem perder sua forma. Para entender melhor o fenômeno de ressonância exibido nesses modelos, construímos um modelo simplificado onde o modo de vibração do kink se torna um modo quasinormal. Isso acarreta na supressão das janelas de ressonância e, consequentemente, na perda da estrutura fractal formada pelas mesmas. Já no caso em que o pontencial do campo escalar é um polinômio de ordem alta, a cauda do kink pode ser de longo alcance, por decair como uma lei de potência. Nós desenvolvemos um método numérico para inicializar esses sistemas corretamente e aplicamos a um modelo de kinks com caudas longas em ambos os lados. Após a colisão, o sistema se aniquila para velocidades abaixo de uma velocidade crítica ultra-relativística e não forma bions. Também investigamos uma colisão entre kinks vibrantes dentro do modelo sine-Gordon duplo. Um dos efeitos de excitar o modo de vibração antes da colisão é a formação de janelas de ressonância onde ocorre apenas um contato entre os kinks. Já na segunda metade da tese, focamos em interações entre kinks e férmions. Estudamos o que acontece com o férmion quando ele se liga a um kink que está vibrando. O férmion escapa do kink na forma de radiação a uma taxa contínua se a diferença de energia entre o estado inicial e o contínuo não for muito grande. Por último, nós investigamos a interação de um férmion na presença de um campo escalar com uma impureza que preserva metade da propriedade Bogomol’nyi–Prasad–Sommerfield (BPS) do sistema. O resultado desse processo é que perto do regime BPS a evolução do sistema é adiabática, pois sempre corresponde a uma solução BPS estática.porUniversidade Federal de PernambucoPrograma de Pos Graduacao em FisicaUFPEBrasilAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessFísica teórica e computacionalDefeito topológicoTeoria de camposKinkInteractions between topological defects in (1+1) dimensionsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisdoutoradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPEORIGINALTESE João Guilherme Ferreira Campos.pdfTESE João Guilherme Ferreira Campos.pdfapplication/pdf4799246https://repositorio.ufpe.br/bitstream/123456789/44502/1/TESE%20Jo%c3%a3o%20Guilherme%20Ferreira%20Campos.pdf78c255b507647d36b50d3b80c8d5e17fMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-82142https://repositorio.ufpe.br/bitstream/123456789/44502/3/license.txt6928b9260b07fb2755249a5ca9903395MD53CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufpe.br/bitstream/123456789/44502/2/license_rdfe39d27027a6cc9cb039ad269a5db8e34MD52TEXTTESE João Guilherme Ferreira Campos.pdf.txtTESE João Guilherme Ferreira Campos.pdf.txtExtracted texttext/plain256108https://repositorio.ufpe.br/bitstream/123456789/44502/4/TESE%20Jo%c3%a3o%20Guilherme%20Ferreira%20Campos.pdf.txt2cdb7cd057be9a6ee9656dc5ef226017MD54THUMBNAILTESE João Guilherme Ferreira Campos.pdf.jpgTESE João Guilherme Ferreira Campos.pdf.jpgGenerated Thumbnailimage/jpeg1225https://repositorio.ufpe.br/bitstream/123456789/44502/5/TESE%20Jo%c3%a3o%20Guilherme%20Ferreira%20Campos.pdf.jpgb47c60be40a7894ab77749a34794c84dMD55123456789/445022022-05-19 02:20:30.461oai:repositorio.ufpe.br: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ório InstitucionalPUBhttps://repositorio.ufpe.br/oai/requestattena@ufpe.bropendoar:22212022-05-19T05:20:30Repositório Institucional da UFPE - Universidade Federal de Pernambuco (UFPE)false |
dc.title.pt_BR.fl_str_mv |
Interactions between topological defects in (1+1) dimensions |
title |
Interactions between topological defects in (1+1) dimensions |
spellingShingle |
Interactions between topological defects in (1+1) dimensions CAMPOS, João Guilherme Ferreira Física teórica e computacional Defeito topológico Teoria de campos Kink |
title_short |
Interactions between topological defects in (1+1) dimensions |
title_full |
Interactions between topological defects in (1+1) dimensions |
title_fullStr |
Interactions between topological defects in (1+1) dimensions |
title_full_unstemmed |
Interactions between topological defects in (1+1) dimensions |
title_sort |
Interactions between topological defects in (1+1) dimensions |
author |
CAMPOS, João Guilherme Ferreira |
author_facet |
CAMPOS, João Guilherme Ferreira |
author_role |
author |
dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/6341109305242477 |
dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/4017443371706337 |
dc.contributor.author.fl_str_mv |
CAMPOS, João Guilherme Ferreira |
dc.contributor.advisor1.fl_str_mv |
MOHAMMADI, Azadeh |
contributor_str_mv |
MOHAMMADI, Azadeh |
dc.subject.por.fl_str_mv |
Física teórica e computacional Defeito topológico Teoria de campos Kink |
topic |
Física teórica e computacional Defeito topológico Teoria de campos Kink |
description |
In this thesis, we study interactions between topological defects in two-dimensional spacetimes. These defects are called kinks. They are solutions of scalar field theories with localized energy which propagate without losing its shape. In order to understand the resonance phenomenon exhibited by those models, we built a toy model where the kink’s vibrational mode turns into a quasinormal mode. This causes the suppression of resonance windows and, consequently, its fractal structure is lost. Considering a higher order polynomial as the scalar field potential, we find kinks with long-range tails, which decay as a power law. We developed a numerical method to correctly initialize this systems and applied it to a scalar field model containing kinks with long-range tails in both sides. After the collision, the kink-antikink pair is annihilated for velocities below an ultra-relativistic critical velocity without bion formation. We also investigated a collision between wobbling kinks of the double sine-Gordon model. When the kinks are already wobbling before colliding, there appears resonance windows with separation after a single bounce. On the second half of the thesis, we focused on fermion-kink interactions. We studied what happens when a fermion binds to a wobbling kink. The result is that the fermion escapes from the kink as radiation and at a constant rate. This occurs if the energy gap between the initial state and the continuum threshold is not too large. Lastly, we investigated the interaction of a fermion with a background scalar field with an impurity that preserves half of the Bogomol’nyi–Prasad–Sommerfield (BPS) property. We found an adiabatic evolution near the BPS regime, which means that the system is at a static BPS solution at every moment. |
publishDate |
2022 |
dc.date.accessioned.fl_str_mv |
2022-05-18T17:09:39Z |
dc.date.available.fl_str_mv |
2022-05-18T17:09:39Z |
dc.date.issued.fl_str_mv |
2022-02-22 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
CAMPOS, João Guilherme Ferreira. Interactions between topological defects in (1+1) dimensions. 2022. Tese (Doutorado em Física) - Universidade Federal de Pernambuco, Recife, 2022. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufpe.br/handle/123456789/44502 |
identifier_str_mv |
CAMPOS, João Guilherme Ferreira. Interactions between topological defects in (1+1) dimensions. 2022. Tese (Doutorado em Física) - Universidade Federal de Pernambuco, Recife, 2022. |
url |
https://repositorio.ufpe.br/handle/123456789/44502 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
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Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
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openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
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Programa de Pos Graduacao em Fisica |
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UFPE |
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Brasil |
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Universidade Federal de Pernambuco |
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