Improving the computation of the τVI Painlevé function using the quadrature method for the fredholm determinant

Detalhes bibliográficos
Ano de defesa: 2020
Autor(a) principal: ANTONIO JUNIOR, Ériton Araujo
Orientador(a): CUNHA, Bruno Geraldo Carneiro da
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: eng
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:
Painlevé VI
Determinante de Fredholm
Problema de Riemann-Hilbert
Problema de parâmetro acessório
Link de acesso: https://repositorio.ufpe.br/handle/123456789/40940
Resumo: The Painlevé transcendent functions are important tools in theoretical physics, they appear in a variety of physical systems going from quantum integrable systems to random matrix theory. The accessory parameter problem for ODEs, which has connections to black hole scattering problem, can be solved by using the connection between the Painlevé VI transcendent with isomonodromic deformations of a linear ordinary differential equation. In this case, the isomonodromic V I function plays a major role, and finding its roots is equivalent to solving the accessory parameter problem. The V I function can be expressed as a function of a Fredholm determinant. In this dissertation, we will discuss the two main different methods of calculation of the V I in the Fredholm determinant form. We will also present how to construct codes for both methods and analyze them in order to understand which one is the most numerically efficient to find the roots of the V I function.
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spelling ANTONIO JUNIOR, Ériton Araujohttp://lattes.cnpq.br/5401411536820923http://lattes.cnpq.br/8859998369703134CUNHA, Bruno Geraldo Carneiro da2021-08-11T22:02:09Z2021-08-11T22:02:09Z2020-03-31ANTONIO JÚNIOR, Ériton Araujo. Improving the computation of the τVI Painlevé function using the quadrature method for the fredholm determinant. 2020. Dissertação (Mestrado em Física) - Universidade Federal de Pernambuco, Recife, 2020.https://repositorio.ufpe.br/handle/123456789/40940The Painlevé transcendent functions are important tools in theoretical physics, they appear in a variety of physical systems going from quantum integrable systems to random matrix theory. The accessory parameter problem for ODEs, which has connections to black hole scattering problem, can be solved by using the connection between the Painlevé VI transcendent with isomonodromic deformations of a linear ordinary differential equation. In this case, the isomonodromic V I function plays a major role, and finding its roots is equivalent to solving the accessory parameter problem. The V I function can be expressed as a function of a Fredholm determinant. In this dissertation, we will discuss the two main different methods of calculation of the V I in the Fredholm determinant form. We will also present how to construct codes for both methods and analyze them in order to understand which one is the most numerically efficient to find the roots of the V I function.CNPqAs funções transcendentais de Painlevé são ferramentas importantes dentro da física teórica, elas aparecem em uma variedade de sistemas físicos indo de sistemas quânticos integráveis à teoria de matrizes aleatórias. O problema dos parâmetros acessórios, que tem conexões com o problema de espalhamento em buracos negros, pode ser resolvido usando a conexão entre as funções transcendentais de Painlevé com as transformações isomonodrômicas em uma equação diferencial ordinária linear. Neste caso a função isomonodrômica V I é de grande importância, e encontrar as raízes de tal função é equivalente a resolver o problema de parâmetro acessório. A função V I pode ser expressada em termos de um determinante de Fredholm. Nesta dissertação serão discutidos os dois principais métodos de se calcular a função V I na sua forma de determinante de Fredholm. Também será apresentado como construir códigos utilizando ambos os métodos e tais códigos serão analisados de maneira a se entender qual dos dois é mais numericamente eficiente para o cálculo das raízes da função V I.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em FisicaUFPEBrasilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessPainlevé VIDeterminante de FredholmProblema de Riemann-HilbertProblema de parâmetro acessórioImproving the computation of the τVI Painlevé function using the quadrature method for the fredholm determinantinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesismestradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPEORIGINALDISSERTAÇÃO Ériton Araujo Antonio Júnior.pdfDISSERTAÇÃO Ériton Araujo Antonio Júnior.pdfapplication/pdf2062642https://repositorio.ufpe.br/bitstream/123456789/40940/1/DISSERTA%c3%87%c3%83O%20%c3%89riton%20Araujo%20Antonio%20J%c3%banior.pdf38e3388f2ed5a97aada9a8750884ffdaMD51LICENSElicense.txtlicense.txttext/plain; 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dc.title.pt_BR.fl_str_mv Improving the computation of the τVI Painlevé function using the quadrature method for the fredholm determinant
title Improving the computation of the τVI Painlevé function using the quadrature method for the fredholm determinant
spellingShingle Improving the computation of the τVI Painlevé function using the quadrature method for the fredholm determinant
ANTONIO JUNIOR, Ériton Araujo
Painlevé VI
Determinante de Fredholm
Problema de Riemann-Hilbert
Problema de parâmetro acessório
title_short Improving the computation of the τVI Painlevé function using the quadrature method for the fredholm determinant
title_full Improving the computation of the τVI Painlevé function using the quadrature method for the fredholm determinant
title_fullStr Improving the computation of the τVI Painlevé function using the quadrature method for the fredholm determinant
title_full_unstemmed Improving the computation of the τVI Painlevé function using the quadrature method for the fredholm determinant
title_sort Improving the computation of the τVI Painlevé function using the quadrature method for the fredholm determinant
author ANTONIO JUNIOR, Ériton Araujo
author_facet ANTONIO JUNIOR, Ériton Araujo
author_role author
dc.contributor.authorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/5401411536820923
dc.contributor.advisorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/8859998369703134
dc.contributor.author.fl_str_mv ANTONIO JUNIOR, Ériton Araujo
dc.contributor.advisor1.fl_str_mv CUNHA, Bruno Geraldo Carneiro da
contributor_str_mv CUNHA, Bruno Geraldo Carneiro da
dc.subject.por.fl_str_mv Painlevé VI
Determinante de Fredholm
Problema de Riemann-Hilbert
Problema de parâmetro acessório
topic Painlevé VI
Determinante de Fredholm
Problema de Riemann-Hilbert
Problema de parâmetro acessório
description The Painlevé transcendent functions are important tools in theoretical physics, they appear in a variety of physical systems going from quantum integrable systems to random matrix theory. The accessory parameter problem for ODEs, which has connections to black hole scattering problem, can be solved by using the connection between the Painlevé VI transcendent with isomonodromic deformations of a linear ordinary differential equation. In this case, the isomonodromic V I function plays a major role, and finding its roots is equivalent to solving the accessory parameter problem. The V I function can be expressed as a function of a Fredholm determinant. In this dissertation, we will discuss the two main different methods of calculation of the V I in the Fredholm determinant form. We will also present how to construct codes for both methods and analyze them in order to understand which one is the most numerically efficient to find the roots of the V I function.
publishDate 2020
dc.date.issued.fl_str_mv 2020-03-31
dc.date.accessioned.fl_str_mv 2021-08-11T22:02:09Z
dc.date.available.fl_str_mv 2021-08-11T22:02:09Z
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 ANTONIO JÚNIOR, Ériton Araujo. Improving the computation of the τVI Painlevé function using the quadrature method for the fredholm determinant. 2020. Dissertação (Mestrado em Física) - Universidade Federal de Pernambuco, Recife, 2020.
dc.identifier.uri.fl_str_mv https://repositorio.ufpe.br/handle/123456789/40940
identifier_str_mv ANTONIO JÚNIOR, Ériton Araujo. Improving the computation of the τVI Painlevé function using the quadrature method for the fredholm determinant. 2020. Dissertação (Mestrado em Física) - Universidade Federal de Pernambuco, Recife, 2020.
url https://repositorio.ufpe.br/handle/123456789/40940
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv http://creativecommons.org/licenses/by-nc-nd/3.0/br/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-nd/3.0/br/
eu_rights_str_mv openAccess
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
dc.publisher.country.fl_str_mv Brasil
publisher.none.fl_str_mv Universidade Federal de Pernambuco
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFPE
instname:Universidade Federal de Pernambuco (UFPE)
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