Unveiling the universal class categorization of Altland-Zirnbauer in mesoscopic systems: probing entanglement and conductance fluctuations
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da UFPB |
Texto Completo: | https://repositorio.ufpb.br/jspui/handle/123456789/29370 |
Resumo: | In this thesis, we present the ten classes of Altland-Zirnbauer symmetry and how they are used to describe universal quantum transport in mesoscopic systems, particularly chaotic quantum dots. We perform numerical simulations using Random Matrix Theory (RMT) to explore transport properties such as conductance and shot noise power, as well as entanglement quantifiers including concurrence, entanglement formation, and Bell inequality. We begin by introducing the description of our system, the chaotic quantum billiard. Then, we derive the MahauxWeidenmüller formula for the scattering matrix, and consequently, the conductance and shot noise power. We then present the possible fundamental symmetries present in mesoscopic systems, such as time-reversal symmetry, spin rotation, chirality, and particle-hole symmetry. In this way, we explore how these symmetries impose constraints on the Hamiltonian and, consequently, the scattering matrix. Finally, we present numerical results showing the influence of these fundamental symmetries on transport and entanglement properties. We provide a statistical analysis of the conductance and shot noise power for Schrödinger, Dirac, and Andreev billiards. Specifically, we observe that chiral and particle-hole symmetries play a role in the universal conductance fluctuations. In addition to transport properties, we perform numerical simulations of quantum entanglement in chaotic quantum billiards. We observe violations of the Bell inequality for all billiards and analyze their dependencies on the number of resonances and barrier transparency. We demonstrate that it is easier to violate the Bell inequality in chiral/sublattice and particle-hole degrees of freedom than in orbital degrees of freedom. Moreover, our results exhibit a unique and peculiar behavior: the realization of entanglement in the Andreev billiard always results in the production of Bell pairs in the single-channel limit, regardless of the presence of time-reversal symmetry and tunneling rates. The entangled pairs are formed by Majorana modes in an interface of different topological phases and may serve as a useful tool for entanglement generation and control, as well as quantum computing. |
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Unveiling the universal class categorization of Altland-Zirnbauer in mesoscopic systems: probing entanglement and conductance fluctuationsFísicaClassificação de Altland-ZirnbauerTeoria de matrizes aleatóriasEmaranhamento quânticoDesigualdade de BellPicos de CondutânciaPotêcia do Ruído de DisparoTenfold wayAltland-Zirnbauer classificationRandom-Matrix TheoryConductance PeaksShot Noise PowerQuantum EntanglementBell’s inequalityCNPQ::CIENCIAS EXATAS E DA TERRA::FISICAIn this thesis, we present the ten classes of Altland-Zirnbauer symmetry and how they are used to describe universal quantum transport in mesoscopic systems, particularly chaotic quantum dots. We perform numerical simulations using Random Matrix Theory (RMT) to explore transport properties such as conductance and shot noise power, as well as entanglement quantifiers including concurrence, entanglement formation, and Bell inequality. We begin by introducing the description of our system, the chaotic quantum billiard. Then, we derive the MahauxWeidenmüller formula for the scattering matrix, and consequently, the conductance and shot noise power. We then present the possible fundamental symmetries present in mesoscopic systems, such as time-reversal symmetry, spin rotation, chirality, and particle-hole symmetry. In this way, we explore how these symmetries impose constraints on the Hamiltonian and, consequently, the scattering matrix. Finally, we present numerical results showing the influence of these fundamental symmetries on transport and entanglement properties. We provide a statistical analysis of the conductance and shot noise power for Schrödinger, Dirac, and Andreev billiards. Specifically, we observe that chiral and particle-hole symmetries play a role in the universal conductance fluctuations. In addition to transport properties, we perform numerical simulations of quantum entanglement in chaotic quantum billiards. We observe violations of the Bell inequality for all billiards and analyze their dependencies on the number of resonances and barrier transparency. We demonstrate that it is easier to violate the Bell inequality in chiral/sublattice and particle-hole degrees of freedom than in orbital degrees of freedom. Moreover, our results exhibit a unique and peculiar behavior: the realization of entanglement in the Andreev billiard always results in the production of Bell pairs in the single-channel limit, regardless of the presence of time-reversal symmetry and tunneling rates. The entangled pairs are formed by Majorana modes in an interface of different topological phases and may serve as a useful tool for entanglement generation and control, as well as quantum computing.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESNeste trabalho, exploramos o uso das dez classes de simetria de Altland-Zirnbauer para descrever o transporte quântico em sistemas mesoscópicos, focando em pontos quânticos caóticos. Utilizamos simulações numéricas baseadas na Teoria de Matrizes Aleatórias (RMT) para investigar propriedades de transporte, como condutância e potência do ruído de disparo, além de quantificadores de emaranhamento, como concorrência, emaranhamento de formação e desigualdade de Bell. Iniciamos apresentando o sistema de estudo, o bilhar quântico caótico, e derivamos a fórmula de Mahaux-Weindenmüller para a matriz de espalhamento. Assim, introduzimos os principais observáveis do transporte quântico: a condutância e o ruído de disparo. Em seguida, exploramos as simetrias fundamentais presentes em sistemas mesoscópicos, como a simetria de reversão temporal, rotação de spin, quiralidade e partícula-buraco, analisando como essas simetrias impõem restrições ao hamiltoniano e à matriz de espalhamento. Em seguida, apresentamos resultados numéricos que destacam a influência dessas simetrias nas propriedades de transporte e emaranhamento. Realizamos uma análise estatística da condutância e do ruído de disparo para bilhares de Schrödinger, Dirac e Andreev, revelando o papel das simetrias quirais e de partícula-buraco nas flutuações universais da condutância. Além disso, investigamos o emaranhamento quântico em bilhares quânticos caóticos, observando violações da desigualdade de Bell em todos os casos, com dependências específicas em relação ao número de ressonâncias e transparência da barreira. Destacamos que é mais fácil violar a desigualdade de Bell nos graus de liberdade quiral/sub-rede e partículas-buraco do que nos graus de liberdade orbitais. Por fim, evidenciamos um comportamento único e intrigante: no bilhar de Andreev, a realização do emaranhamento sempre resulta na produção de pares de Bell no limite de canal único, independentemente da presença da simetria de reversão temporal e das taxas de tunelamento. Esses pares emaranhados são formados por modos de Majorana em interfaces de diferentes fases topológicas, sugerindo sua utilidade como ferramenta para produção e controle de emaranhamento, bem como para aplicações em computação quântica.Universidade Federal da ParaíbaBrasilFísicaPrograma de Pós-Graduação em FísicaUFPBRamos, Jorge Gabriel Gomes de Souzahttp://lattes.cnpq.br/4289978259221930Batista, Rafael Alves2024-01-29T22:25:37Z2023-08-092024-01-29T22:25:37Z2023-07-18info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesishttps://repositorio.ufpb.br/jspui/handle/123456789/29370porAttribution-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nd/3.0/br/info:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da UFPBinstname:Universidade Federal da Paraíba (UFPB)instacron:UFPB2024-01-30T06:08:55Zoai:repositorio.ufpb.br:123456789/29370Biblioteca Digital de Teses e Dissertaçõeshttps://repositorio.ufpb.br/PUBhttp://tede.biblioteca.ufpb.br:8080/oai/requestdiretoria@ufpb.br|| diretoria@ufpb.bropendoar:2024-01-30T06:08:55Biblioteca Digital de Teses e Dissertações da UFPB - Universidade Federal da Paraíba (UFPB)false |
dc.title.none.fl_str_mv |
Unveiling the universal class categorization of Altland-Zirnbauer in mesoscopic systems: probing entanglement and conductance fluctuations |
title |
Unveiling the universal class categorization of Altland-Zirnbauer in mesoscopic systems: probing entanglement and conductance fluctuations |
spellingShingle |
Unveiling the universal class categorization of Altland-Zirnbauer in mesoscopic systems: probing entanglement and conductance fluctuations Batista, Rafael Alves Física Classificação de Altland-Zirnbauer Teoria de matrizes aleatórias Emaranhamento quântico Desigualdade de Bell Picos de Condutância Potêcia do Ruído de Disparo Tenfold way Altland-Zirnbauer classification Random-Matrix Theory Conductance Peaks Shot Noise Power Quantum Entanglement Bell’s inequality CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA |
title_short |
Unveiling the universal class categorization of Altland-Zirnbauer in mesoscopic systems: probing entanglement and conductance fluctuations |
title_full |
Unveiling the universal class categorization of Altland-Zirnbauer in mesoscopic systems: probing entanglement and conductance fluctuations |
title_fullStr |
Unveiling the universal class categorization of Altland-Zirnbauer in mesoscopic systems: probing entanglement and conductance fluctuations |
title_full_unstemmed |
Unveiling the universal class categorization of Altland-Zirnbauer in mesoscopic systems: probing entanglement and conductance fluctuations |
title_sort |
Unveiling the universal class categorization of Altland-Zirnbauer in mesoscopic systems: probing entanglement and conductance fluctuations |
author |
Batista, Rafael Alves |
author_facet |
Batista, Rafael Alves |
author_role |
author |
dc.contributor.none.fl_str_mv |
Ramos, Jorge Gabriel Gomes de Souza http://lattes.cnpq.br/4289978259221930 |
dc.contributor.author.fl_str_mv |
Batista, Rafael Alves |
dc.subject.por.fl_str_mv |
Física Classificação de Altland-Zirnbauer Teoria de matrizes aleatórias Emaranhamento quântico Desigualdade de Bell Picos de Condutância Potêcia do Ruído de Disparo Tenfold way Altland-Zirnbauer classification Random-Matrix Theory Conductance Peaks Shot Noise Power Quantum Entanglement Bell’s inequality CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA |
topic |
Física Classificação de Altland-Zirnbauer Teoria de matrizes aleatórias Emaranhamento quântico Desigualdade de Bell Picos de Condutância Potêcia do Ruído de Disparo Tenfold way Altland-Zirnbauer classification Random-Matrix Theory Conductance Peaks Shot Noise Power Quantum Entanglement Bell’s inequality CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA |
description |
In this thesis, we present the ten classes of Altland-Zirnbauer symmetry and how they are used to describe universal quantum transport in mesoscopic systems, particularly chaotic quantum dots. We perform numerical simulations using Random Matrix Theory (RMT) to explore transport properties such as conductance and shot noise power, as well as entanglement quantifiers including concurrence, entanglement formation, and Bell inequality. We begin by introducing the description of our system, the chaotic quantum billiard. Then, we derive the MahauxWeidenmüller formula for the scattering matrix, and consequently, the conductance and shot noise power. We then present the possible fundamental symmetries present in mesoscopic systems, such as time-reversal symmetry, spin rotation, chirality, and particle-hole symmetry. In this way, we explore how these symmetries impose constraints on the Hamiltonian and, consequently, the scattering matrix. Finally, we present numerical results showing the influence of these fundamental symmetries on transport and entanglement properties. We provide a statistical analysis of the conductance and shot noise power for Schrödinger, Dirac, and Andreev billiards. Specifically, we observe that chiral and particle-hole symmetries play a role in the universal conductance fluctuations. In addition to transport properties, we perform numerical simulations of quantum entanglement in chaotic quantum billiards. We observe violations of the Bell inequality for all billiards and analyze their dependencies on the number of resonances and barrier transparency. We demonstrate that it is easier to violate the Bell inequality in chiral/sublattice and particle-hole degrees of freedom than in orbital degrees of freedom. Moreover, our results exhibit a unique and peculiar behavior: the realization of entanglement in the Andreev billiard always results in the production of Bell pairs in the single-channel limit, regardless of the presence of time-reversal symmetry and tunneling rates. The entangled pairs are formed by Majorana modes in an interface of different topological phases and may serve as a useful tool for entanglement generation and control, as well as quantum computing. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-08-09 2023-07-18 2024-01-29T22:25:37Z 2024-01-29T22:25:37Z |
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://repositorio.ufpb.br/jspui/handle/123456789/29370 |
url |
https://repositorio.ufpb.br/jspui/handle/123456789/29370 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.rights.driver.fl_str_mv |
Attribution-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nd/3.0/br/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Attribution-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nd/3.0/br/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal da Paraíba Brasil Física Programa de Pós-Graduação em Física UFPB |
publisher.none.fl_str_mv |
Universidade Federal da Paraíba Brasil Física Programa de Pós-Graduação em Física UFPB |
dc.source.none.fl_str_mv |
reponame:Biblioteca Digital de Teses e Dissertações da UFPB instname:Universidade Federal da Paraíba (UFPB) instacron:UFPB |
instname_str |
Universidade Federal da Paraíba (UFPB) |
instacron_str |
UFPB |
institution |
UFPB |
reponame_str |
Biblioteca Digital de Teses e Dissertações da UFPB |
collection |
Biblioteca Digital de Teses e Dissertações da UFPB |
repository.name.fl_str_mv |
Biblioteca Digital de Teses e Dissertações da UFPB - Universidade Federal da Paraíba (UFPB) |
repository.mail.fl_str_mv |
diretoria@ufpb.br|| diretoria@ufpb.br |
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1801843015429390336 |