Multiconfigurational Hartree method for many-particle systems
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da USP |
Texto Completo: | https://doi.org/10.11606/T.43.2022.tde-30032022-100240 |
Resumo: | In the present thesis, the multiconfigurational time-dependent Hartree method is applied to study flow properties of bosons trapped in annular geometry. This physical system provides a suitable platform to investigate beyond meanfield features, since as one spatial dimensional problem, we can explore different interacting regimes, set a rather large range for parameter values without excessive concern about the computational cost and explore relevant concepts, such as superfluidity. As a very important part of the present thesis, the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) is carefully described, providing all relevant derivations up to the final equations of motion, as well as a prospectus of the numerical approach. As such, this thesis also deals with topics of numerical analysis due to its method complexity. After the MCTDHB derivation and its numerical implementation are shown, the superfluid properties of a bosonic gas in annular geometry are studied with the most general approach proposed in reference [1], without any assumptions about the condensation status of the system. In addition, the MCTDHBs capability to provide correlation functions is exploited to characterize the loss of superfluid fraction due to a potential barrier. Within the same goal to study bosonic flow properties in a ring, persistent currents are also investigated, with two alternative derivations for the metastability condition as energy local minimum. Besides, the dynamical decay of the current is analyzed after quenching a potential barrier. Fluctuations of the number operator and probabilities are calculated along the time evolution to provide information about the quantum statistical distribution embedded in experimental measures, aiming to spot relevant information on image observation of flowing states. |
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info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis Multiconfigurational Hartree method for many-particle systems Método de Hartree multiconfiguracional para sistemas de muitas partículas 2022-03-11Arnaldo GammalTommaso MacriCaetano Rodrigues MirandaMonica Andrioli Caracanhas SantarelliPeter SchmelcherAlex Valerio AndriatiUniversidade de São PauloFísicaUSPBR Bose-Einstein condensation bosons bósons condensação de Bose-Einstein many-particle system método de Hartree multiconfiguracional Multiconfigurational Hartree method sistemas de muitas partculas superfluid superfluido. In the present thesis, the multiconfigurational time-dependent Hartree method is applied to study flow properties of bosons trapped in annular geometry. This physical system provides a suitable platform to investigate beyond meanfield features, since as one spatial dimensional problem, we can explore different interacting regimes, set a rather large range for parameter values without excessive concern about the computational cost and explore relevant concepts, such as superfluidity. As a very important part of the present thesis, the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) is carefully described, providing all relevant derivations up to the final equations of motion, as well as a prospectus of the numerical approach. As such, this thesis also deals with topics of numerical analysis due to its method complexity. After the MCTDHB derivation and its numerical implementation are shown, the superfluid properties of a bosonic gas in annular geometry are studied with the most general approach proposed in reference [1], without any assumptions about the condensation status of the system. In addition, the MCTDHBs capability to provide correlation functions is exploited to characterize the loss of superfluid fraction due to a potential barrier. Within the same goal to study bosonic flow properties in a ring, persistent currents are also investigated, with two alternative derivations for the metastability condition as energy local minimum. Besides, the dynamical decay of the current is analyzed after quenching a potential barrier. Fluctuations of the number operator and probabilities are calculated along the time evolution to provide information about the quantum statistical distribution embedded in experimental measures, aiming to spot relevant information on image observation of flowing states. Nesta tese, o método de Hartree multiconfiguracional dependente do tempo é aplicado para estudar a circulação de bósons armadilhados em geometria anular. Este sistema físico oferece uma plataforma adequada para investigar características além do escopo de campo médio, uma vez que sendo em uma dimensão espacial, podemos explorar diferentes regimes de interação, estabelecer um longo alcance para valores dos parâmetros sem demasiadas preocupações com o custo computacional e explorar conceitos relevantes, como a superfluidez. Como uma parte muito importante da presente tese, o método de Hartree multiconfiguracional dependente do tempo para bósons (MCTDHB) é cuidadosamente descrito, fornecendo todas derivações relevantes até as equações finais de movimento, bem como um prospecto para abordagem numérica. Assim sendo, esta tese também trata de tópicos de análise numérica devido a complexidade do método envolvido. Após a derivação do MCTDHB e sua implementação numérica serem mostradas, as propriedades superfluídas de um gás bosônico em geometria anular foram estudadas com a maior generalidade possível proposta na referência [1], sem qualquer suposição sobre o estado de condensação do sistema. Além disso, a capacidade do MCTDHB de fornecer funções de correlação é explorada para caracterizar a perda da fração de superfluido devido a um barreira. Ainda dentro do mesmo objetivo de estudar propriedades de circulação bosônicas em um anel, correntes persistentes também são investigadas, com duas derivações alternativas para condição de meta-estabilidade como um mínimo local para energia. Ademais, o decaimento dinâmico da corrente é analisado após abruptamente introduzir uma barreira como potencial. Flutuações do operador de número e probabilidades são calculadas ao longo da evolução temporal para fornecer informações sobre a distribuição estatística quântica em medidas experimentais, objetivando revelar informações relevantes sobre a observação por imagem de estados com circulação. https://doi.org/10.11606/T.43.2022.tde-30032022-100240info:eu-repo/semantics/openAccessengreponame:Biblioteca Digital de Teses e Dissertações da USPinstname:Universidade de São Paulo (USP)instacron:USP2023-12-21T20:25:54Zoai:teses.usp.br:tde-30032022-100240Biblioteca Digital de Teses e Dissertaçõeshttp://www.teses.usp.br/PUBhttp://www.teses.usp.br/cgi-bin/mtd2br.plvirginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.bropendoar:27212023-12-22T13:31:30.050487Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP)false |
dc.title.en.fl_str_mv |
Multiconfigurational Hartree method for many-particle systems |
dc.title.alternative.pt.fl_str_mv |
Método de Hartree multiconfiguracional para sistemas de muitas partículas |
title |
Multiconfigurational Hartree method for many-particle systems |
spellingShingle |
Multiconfigurational Hartree method for many-particle systems Alex Valerio Andriati |
title_short |
Multiconfigurational Hartree method for many-particle systems |
title_full |
Multiconfigurational Hartree method for many-particle systems |
title_fullStr |
Multiconfigurational Hartree method for many-particle systems |
title_full_unstemmed |
Multiconfigurational Hartree method for many-particle systems |
title_sort |
Multiconfigurational Hartree method for many-particle systems |
author |
Alex Valerio Andriati |
author_facet |
Alex Valerio Andriati |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Arnaldo Gammal |
dc.contributor.referee1.fl_str_mv |
Tommaso Macri |
dc.contributor.referee2.fl_str_mv |
Caetano Rodrigues Miranda |
dc.contributor.referee3.fl_str_mv |
Monica Andrioli Caracanhas Santarelli |
dc.contributor.referee4.fl_str_mv |
Peter Schmelcher |
dc.contributor.author.fl_str_mv |
Alex Valerio Andriati |
contributor_str_mv |
Arnaldo Gammal Tommaso Macri Caetano Rodrigues Miranda Monica Andrioli Caracanhas Santarelli Peter Schmelcher |
description |
In the present thesis, the multiconfigurational time-dependent Hartree method is applied to study flow properties of bosons trapped in annular geometry. This physical system provides a suitable platform to investigate beyond meanfield features, since as one spatial dimensional problem, we can explore different interacting regimes, set a rather large range for parameter values without excessive concern about the computational cost and explore relevant concepts, such as superfluidity. As a very important part of the present thesis, the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) is carefully described, providing all relevant derivations up to the final equations of motion, as well as a prospectus of the numerical approach. As such, this thesis also deals with topics of numerical analysis due to its method complexity. After the MCTDHB derivation and its numerical implementation are shown, the superfluid properties of a bosonic gas in annular geometry are studied with the most general approach proposed in reference [1], without any assumptions about the condensation status of the system. In addition, the MCTDHBs capability to provide correlation functions is exploited to characterize the loss of superfluid fraction due to a potential barrier. Within the same goal to study bosonic flow properties in a ring, persistent currents are also investigated, with two alternative derivations for the metastability condition as energy local minimum. Besides, the dynamical decay of the current is analyzed after quenching a potential barrier. Fluctuations of the number operator and probabilities are calculated along the time evolution to provide information about the quantum statistical distribution embedded in experimental measures, aiming to spot relevant information on image observation of flowing states. |
publishDate |
2022 |
dc.date.issued.fl_str_mv |
2022-03-11 |
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.uri.fl_str_mv |
https://doi.org/10.11606/T.43.2022.tde-30032022-100240 |
url |
https://doi.org/10.11606/T.43.2022.tde-30032022-100240 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade de São Paulo |
dc.publisher.program.fl_str_mv |
Física |
dc.publisher.initials.fl_str_mv |
USP |
dc.publisher.country.fl_str_mv |
BR |
publisher.none.fl_str_mv |
Universidade de São Paulo |
dc.source.none.fl_str_mv |
reponame:Biblioteca Digital de Teses e Dissertações da USP instname:Universidade de São Paulo (USP) instacron:USP |
instname_str |
Universidade de São Paulo (USP) |
instacron_str |
USP |
institution |
USP |
reponame_str |
Biblioteca Digital de Teses e Dissertações da USP |
collection |
Biblioteca Digital de Teses e Dissertações da USP |
repository.name.fl_str_mv |
Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP) |
repository.mail.fl_str_mv |
virginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.br |
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1794503152508076032 |