Estudo termodinâmico de sistemas quânticos caóticos via Teoria de Matrizes Aleatórias

Detalhes bibliográficos
Autor(a) principal: Cavalcante, Eric Gomes Arrais
Data de Publicação: 2016
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UFG
dARK ID: ark:/38995/0013000009q2j
Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/6298
Resumo: Results from classical Random Matrix Theory (RMT) are well recognized as a way to describe spectral statistical properties of classically chaotic quantum systems, such as the level spacing distribution. We investigate, both numerically and analytically, if RMT can be used, at least for some regimes, to predict the behavior of the statistics of work performed by quenching some external parameter dictating the dynamics of a quantum chaotic system. This is done by comparison of the characteristic function of work obtained numerically from a well known quantum chaotic system called Dicke Model and from matrices pertaining to one of the classical ensembles of RMT, namely GOE. We also show one analytical result for the RMT average of the characteristic function that holds in the limit of high temperatures.
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spelling Almeida, Norton Gomes dehttp://lattes.cnpq.br/3182841849332242Céleri, Lucas Chibebehttp://lattes.cnpq.br/6630683190018665Almeida, Norton Gomes deCéleri, Lucas ChibebeAvelar, Ardiley TorresVillas-Bôas, Celso Jorgehttp://lattes.cnpq.br/0207404582902911Cavalcante, Eric Gomes Arrais2016-09-28T12:29:27Z2016-08-22CAVALCANTE, Eric Gomes Arrais. Estudo termodinâmico de sistemas quânticos caóticos via Teoria de Matrizes Aleatórias. 2016. 82 f. Dissertação (Mestrado em Fisica) - Universidade Federal de Goiás, Goiânia, 2016.http://repositorio.bc.ufg.br/tede/handle/tede/6298ark:/38995/0013000009q2jResults from classical Random Matrix Theory (RMT) are well recognized as a way to describe spectral statistical properties of classically chaotic quantum systems, such as the level spacing distribution. We investigate, both numerically and analytically, if RMT can be used, at least for some regimes, to predict the behavior of the statistics of work performed by quenching some external parameter dictating the dynamics of a quantum chaotic system. This is done by comparison of the characteristic function of work obtained numerically from a well known quantum chaotic system called Dicke Model and from matrices pertaining to one of the classical ensembles of RMT, namely GOE. We also show one analytical result for the RMT average of the characteristic function that holds in the limit of high temperatures.É reconhecido que a teoria de matrizes aleatórias (RMT) é capaz de descrever corretamente o comportamento de propriedades estatísticas espectrais de sistemas quânticos classicamente caóticos, como, por exemplo, suas distribuições de espaçamento de níveis. Investigamos, tanto numericamente quanto analiticamente, se a RMT pode ser usada, ao menos em alguns regimes, para predizer o comportamento da estatística do trabalho realizado ao se realizar um quench sobre um parâmetro externo que dita a dinâmica de um sistema quântico caótico. Isso é feito através da comparação da função característica do trabalho obtida numericamente a partir de um sistema quântico caótico bem conhecido, chamado modelo de Dicke, com a obtida a partir de matrizes pertencentes a um dos ensembles clássicos da RMT, chamado GOE. Mostramos também um resultado analítico para a média RMT da função característica que é válida para o limite de altas temperaturas.Submitted by Erika Demachki (erikademachki@gmail.com) on 2016-09-27T18:02:45Z No. of bitstreams: 2 Dissertação - Eric Gomes Arrais Cavalcante - 2016.pdf: 2072393 bytes, checksum: c41dbeb585036af1c9bb4448250b6edd (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-09-28T12:29:27Z (GMT) No. of bitstreams: 2 Dissertação - Eric Gomes Arrais Cavalcante - 2016.pdf: 2072393 bytes, checksum: c41dbeb585036af1c9bb4448250b6edd (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)Made available in DSpace on 2016-09-28T12:29:27Z (GMT). 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dc.title.por.fl_str_mv Estudo termodinâmico de sistemas quânticos caóticos via Teoria de Matrizes Aleatórias
dc.title.alternative.eng.fl_str_mv Thermodynamic study of quantum chaotic system using Random Matrix Theory
title Estudo termodinâmico de sistemas quânticos caóticos via Teoria de Matrizes Aleatórias
spellingShingle Estudo termodinâmico de sistemas quânticos caóticos via Teoria de Matrizes Aleatórias
Cavalcante, Eric Gomes Arrais
Termodinâmica
Caos
Teoria de Matrizes Aleatórias
Thermodynamics
Chaos
Random Matrix Theory
CIENCIAS EXATAS E DA TERRA::FISICA
title_short Estudo termodinâmico de sistemas quânticos caóticos via Teoria de Matrizes Aleatórias
title_full Estudo termodinâmico de sistemas quânticos caóticos via Teoria de Matrizes Aleatórias
title_fullStr Estudo termodinâmico de sistemas quânticos caóticos via Teoria de Matrizes Aleatórias
title_full_unstemmed Estudo termodinâmico de sistemas quânticos caóticos via Teoria de Matrizes Aleatórias
title_sort Estudo termodinâmico de sistemas quânticos caóticos via Teoria de Matrizes Aleatórias
author Cavalcante, Eric Gomes Arrais
author_facet Cavalcante, Eric Gomes Arrais
author_role author
dc.contributor.advisor1.fl_str_mv Almeida, Norton Gomes de
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/3182841849332242
dc.contributor.advisor-co1.fl_str_mv Céleri, Lucas Chibebe
dc.contributor.advisor-co1Lattes.fl_str_mv http://lattes.cnpq.br/6630683190018665
dc.contributor.referee1.fl_str_mv Almeida, Norton Gomes de
dc.contributor.referee2.fl_str_mv Céleri, Lucas Chibebe
dc.contributor.referee3.fl_str_mv Avelar, Ardiley Torres
dc.contributor.referee4.fl_str_mv Villas-Bôas, Celso Jorge
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/0207404582902911
dc.contributor.author.fl_str_mv Cavalcante, Eric Gomes Arrais
contributor_str_mv Almeida, Norton Gomes de
Céleri, Lucas Chibebe
Almeida, Norton Gomes de
Céleri, Lucas Chibebe
Avelar, Ardiley Torres
Villas-Bôas, Celso Jorge
dc.subject.por.fl_str_mv Termodinâmica
Caos
Teoria de Matrizes Aleatórias
topic Termodinâmica
Caos
Teoria de Matrizes Aleatórias
Thermodynamics
Chaos
Random Matrix Theory
CIENCIAS EXATAS E DA TERRA::FISICA
dc.subject.eng.fl_str_mv Thermodynamics
Chaos
Random Matrix Theory
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::FISICA
description Results from classical Random Matrix Theory (RMT) are well recognized as a way to describe spectral statistical properties of classically chaotic quantum systems, such as the level spacing distribution. We investigate, both numerically and analytically, if RMT can be used, at least for some regimes, to predict the behavior of the statistics of work performed by quenching some external parameter dictating the dynamics of a quantum chaotic system. This is done by comparison of the characteristic function of work obtained numerically from a well known quantum chaotic system called Dicke Model and from matrices pertaining to one of the classical ensembles of RMT, namely GOE. We also show one analytical result for the RMT average of the characteristic function that holds in the limit of high temperatures.
publishDate 2016
dc.date.accessioned.fl_str_mv 2016-09-28T12:29:27Z
dc.date.issued.fl_str_mv 2016-08-22
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
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dc.identifier.citation.fl_str_mv CAVALCANTE, Eric Gomes Arrais. Estudo termodinâmico de sistemas quânticos caóticos via Teoria de Matrizes Aleatórias. 2016. 82 f. Dissertação (Mestrado em Fisica) - Universidade Federal de Goiás, Goiânia, 2016.
dc.identifier.uri.fl_str_mv http://repositorio.bc.ufg.br/tede/handle/tede/6298
dc.identifier.dark.fl_str_mv ark:/38995/0013000009q2j
identifier_str_mv CAVALCANTE, Eric Gomes Arrais. Estudo termodinâmico de sistemas quânticos caóticos via Teoria de Matrizes Aleatórias. 2016. 82 f. Dissertação (Mestrado em Fisica) - Universidade Federal de Goiás, Goiânia, 2016.
ark:/38995/0013000009q2j
url http://repositorio.bc.ufg.br/tede/handle/tede/6298
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dc.publisher.none.fl_str_mv Universidade Federal de Goiás
dc.publisher.program.fl_str_mv Programa de Pós-graduação em Fisica (IF)
dc.publisher.initials.fl_str_mv UFG
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv Instituto de Física - IF (RG)
publisher.none.fl_str_mv Universidade Federal de Goiás
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFG
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