A discrete exterior calculus approach to quantum transport on surfaces
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFPE |
Texto Completo: | https://repositorio.ufpe.br/handle/123456789/36046 |
Resumo: | We address the problem of computing transport observables on arbitrary surfaces. Our approach is based on discrete exterior calculus (DEC) and applies to open quantum systems. The curved system is approximated by a simplicial complex consisting of flat triangles where each vertex is located on a smooth surface. Was developed a discretization of Schrödinger equation and the associated Green’s functions. Such an approach allowed for the formulation of the tight-binding Hamiltonian based in discrete calculus exterior. We present an efficient algorithm for the calculation of the recursive Green’s functions using numerical tools available for DEC. In addition to working with curved surfaces, our discretization shares the advantages of the Finite Differences Method when submitted to mesh in flat space. Our approach is applied to the calculation of the conductance of a non-flat quantum device coupled to electron reservoirs defined on curved surfaces. We found numerical evidence of a curvature induced integrablechaotic crossover. |
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SILVA, Leon Denis dahttp://lattes.cnpq.br/2239251029436873http://lattes.cnpq.br/3847692220708299http://lattes.cnpq.br/7160030619369816MELO, Silvio de BarrosMACEDO, Antonio Murilo Santos2020-01-17T12:12:13Z2020-01-17T12:12:13Z2019-10-25SILVA, Leon Denis da. A discrete exterior calculus approach to quantum transport on surfaces. 2019. Tese (Doutorado em Ciência da Computação) – Universidade Federal de Pernambuco, Recife, 2019.https://repositorio.ufpe.br/handle/123456789/36046We address the problem of computing transport observables on arbitrary surfaces. Our approach is based on discrete exterior calculus (DEC) and applies to open quantum systems. The curved system is approximated by a simplicial complex consisting of flat triangles where each vertex is located on a smooth surface. Was developed a discretization of Schrödinger equation and the associated Green’s functions. Such an approach allowed for the formulation of the tight-binding Hamiltonian based in discrete calculus exterior. We present an efficient algorithm for the calculation of the recursive Green’s functions using numerical tools available for DEC. In addition to working with curved surfaces, our discretization shares the advantages of the Finite Differences Method when submitted to mesh in flat space. Our approach is applied to the calculation of the conductance of a non-flat quantum device coupled to electron reservoirs defined on curved surfaces. We found numerical evidence of a curvature induced integrablechaotic crossover.Abordamos o problema de computar observáveis de transporte em superfícies arbitrárias. Nossa abordagem é baseada em cálculo exterior discreto (DEC) e aplica-se a sistemas quânticos abertos. O sistema curvo é aproximado por um simplicial complex que consiste de triângulos planos, onde cada vértice está localizado em uma superfície suave. Foi desenvolvida uma discretização da equação de Schrödinger e das funções de Green associadas. Tal abordagem permitiu a formulação do hamiltoniano, do tipo tight-binding, com base no cálculo exterior discreto. Apresentamos um algoritmo eficiente para o cálculo das curvas recursivas de Green. Além de trabalhar com superfícies curvas, nossa discretização compartilha as vantagens do Método de Diferenças Finitas quando submetido a um domínio plano, nossa abordagem é aplicada ao cálculo da condutância de um dispositivo curvo acoplado a reservatórios de elétrons definidos em superfícies curvas. Encontramos evidências numéricas de um cruzamento caótico-integrável induzido por curvatura.porUniversidade Federal de PernambucoPrograma de Pos Graduacao em Ciencia da ComputacaoUFPEBrasilAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessMídia e InteraçãoCálculo exterior discretoEspalhamento quânticoFunções de Green recursisvasA discrete exterior calculus approach to quantum transport on surfacesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisdoutoradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPEORIGINALTESE Leon Denis da Silva.pdfTESE Leon Denis da Silva.pdfapplication/pdf1213655https://repositorio.ufpe.br/bitstream/123456789/36046/1/TESE%20Leon%20Denis%20da%20Silva.pdf51296ff912d7d6d92b6beb5697ee9d9eMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufpe.br/bitstream/123456789/36046/2/license_rdfe39d27027a6cc9cb039ad269a5db8e34MD52LICENSElicense.txtlicense.txttext/plain; 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dc.title.pt_BR.fl_str_mv |
A discrete exterior calculus approach to quantum transport on surfaces |
title |
A discrete exterior calculus approach to quantum transport on surfaces |
spellingShingle |
A discrete exterior calculus approach to quantum transport on surfaces SILVA, Leon Denis da Mídia e Interação Cálculo exterior discreto Espalhamento quântico Funções de Green recursisvas |
title_short |
A discrete exterior calculus approach to quantum transport on surfaces |
title_full |
A discrete exterior calculus approach to quantum transport on surfaces |
title_fullStr |
A discrete exterior calculus approach to quantum transport on surfaces |
title_full_unstemmed |
A discrete exterior calculus approach to quantum transport on surfaces |
title_sort |
A discrete exterior calculus approach to quantum transport on surfaces |
author |
SILVA, Leon Denis da |
author_facet |
SILVA, Leon Denis da |
author_role |
author |
dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/2239251029436873 |
dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/3847692220708299 |
dc.contributor.advisor-coLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/7160030619369816 |
dc.contributor.author.fl_str_mv |
SILVA, Leon Denis da |
dc.contributor.advisor1.fl_str_mv |
MELO, Silvio de Barros |
dc.contributor.advisor-co1.fl_str_mv |
MACEDO, Antonio Murilo Santos |
contributor_str_mv |
MELO, Silvio de Barros MACEDO, Antonio Murilo Santos |
dc.subject.por.fl_str_mv |
Mídia e Interação Cálculo exterior discreto Espalhamento quântico Funções de Green recursisvas |
topic |
Mídia e Interação Cálculo exterior discreto Espalhamento quântico Funções de Green recursisvas |
description |
We address the problem of computing transport observables on arbitrary surfaces. Our approach is based on discrete exterior calculus (DEC) and applies to open quantum systems. The curved system is approximated by a simplicial complex consisting of flat triangles where each vertex is located on a smooth surface. Was developed a discretization of Schrödinger equation and the associated Green’s functions. Such an approach allowed for the formulation of the tight-binding Hamiltonian based in discrete calculus exterior. We present an efficient algorithm for the calculation of the recursive Green’s functions using numerical tools available for DEC. In addition to working with curved surfaces, our discretization shares the advantages of the Finite Differences Method when submitted to mesh in flat space. Our approach is applied to the calculation of the conductance of a non-flat quantum device coupled to electron reservoirs defined on curved surfaces. We found numerical evidence of a curvature induced integrablechaotic crossover. |
publishDate |
2019 |
dc.date.issued.fl_str_mv |
2019-10-25 |
dc.date.accessioned.fl_str_mv |
2020-01-17T12:12:13Z |
dc.date.available.fl_str_mv |
2020-01-17T12:12:13Z |
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 |
SILVA, Leon Denis da. A discrete exterior calculus approach to quantum transport on surfaces. 2019. Tese (Doutorado em Ciência da Computação) – Universidade Federal de Pernambuco, Recife, 2019. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufpe.br/handle/123456789/36046 |
identifier_str_mv |
SILVA, Leon Denis da. A discrete exterior calculus approach to quantum transport on surfaces. 2019. Tese (Doutorado em Ciência da Computação) – Universidade Federal de Pernambuco, Recife, 2019. |
url |
https://repositorio.ufpe.br/handle/123456789/36046 |
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/ |
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 Ciencia da Computacao |
dc.publisher.initials.fl_str_mv |
UFPE |
dc.publisher.country.fl_str_mv |
Brasil |
publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
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UFPE |
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Repositório Institucional da UFPE |
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