Correlações quânticas em sistemas críticos
Ano de defesa: | 2015 |
---|---|
Autor(a) principal: | |
Orientador(a): | |
Banca de defesa: | , , |
Tipo de documento: | Dissertação |
Tipo de acesso: | Acesso aberto |
Idioma: | por |
Instituição de defesa: |
Universidade Federal de Goiás
|
Programa de Pós-Graduação: |
Programa de Pós-graduação em Fisica (IF)
|
Departamento: |
Instituto de Física - IF (RG)
|
País: |
Brasil
|
Palavras-chave em Português: | |
Palavras-chave em Inglês: | |
Área do conhecimento CNPq: | |
Link de acesso: | http://repositorio.bc.ufg.br/tede/handle/tede/4991 |
Resumo: | Correlations are ubiquitous in nature and have played an extremely important role in human life for a long time. For example, in economy, correlations between price and demand are extremely important for a businessman (or even a government) to make decisions regarding their investment policy. In the field of biology, genetic correlations are central to follow individual characteristics. The relationship between income distribution and crime rate is just one example coming from the social sciences. Mathematically, correlation is a number that describes the degree of relationship between two variables. In the classical domain, this number can be computed in the context of information theory, developed by Shannon in 1948. Focusing on the subject of the present work, the discussion regarding the quantum nature of the correlations permeates physics since Einstein, Podolski and Rosen published their famous article criticizing quantum mechanics. Since then, the so-called quantum correlations have been shown to be a very important tool in the study of many-bodies physics. Another feature of many-body physics is that certain systems, under certain conditions, exhibit what we call quantum phase transition. Such transitions are analogous to the classical transitions, but being governed by purely quantum fluctuations and, as such, may occur at zero temperature, unlike the former, which are guided by thermal fluctuations. One of the main phenomenon that characterizes these transitions is the fact that the correlation length (defined between two subsystems of the global system) highly increases at the transition point. This means that such subsystems can be strongly correlated even if they are separated by a large distance. The main goal of the present work is the study of quantum correlations, specifically the entanglement and the local quantum uncertainty (LQU), in systems presenting one or more quantum phase transitions. Specifically, we consider three models of spin chains: 1) The XY and the XY T, which describes chains of spins- 1=2 —the second considering three spins interaction while the first one takes into account only pairwise interactions; 2) A model describing a chain formed by bosonic spins, i.e. particles with spin-1. As a general conclusion, quantum correlation provides a very powerful tool for the study of critical phenomena, providing, among other things, a means to identify a quantum phase transition. |
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Céleri , Lucas Chibebehttp://lattes.cnpq.br/6630683190018665Céleri, Lucas ChibebeAlmeida, Agnaldo Rosa deAlmeida, Norton Gomes dehttp://lattes.cnpq.br/2627207807532627Nascimento , Andesson Brito2015-12-04T06:59:29Z2015-07-24NASCIMENTO, A. B. Correlações quânticas em sistemas críticos. 2015. 90 f. Dissertação (Mestrado em Física) - Universidade Federal de Goiás, Goiânia, 2015.http://repositorio.bc.ufg.br/tede/handle/tede/4991Correlations are ubiquitous in nature and have played an extremely important role in human life for a long time. For example, in economy, correlations between price and demand are extremely important for a businessman (or even a government) to make decisions regarding their investment policy. In the field of biology, genetic correlations are central to follow individual characteristics. The relationship between income distribution and crime rate is just one example coming from the social sciences. Mathematically, correlation is a number that describes the degree of relationship between two variables. In the classical domain, this number can be computed in the context of information theory, developed by Shannon in 1948. Focusing on the subject of the present work, the discussion regarding the quantum nature of the correlations permeates physics since Einstein, Podolski and Rosen published their famous article criticizing quantum mechanics. Since then, the so-called quantum correlations have been shown to be a very important tool in the study of many-bodies physics. Another feature of many-body physics is that certain systems, under certain conditions, exhibit what we call quantum phase transition. Such transitions are analogous to the classical transitions, but being governed by purely quantum fluctuations and, as such, may occur at zero temperature, unlike the former, which are guided by thermal fluctuations. One of the main phenomenon that characterizes these transitions is the fact that the correlation length (defined between two subsystems of the global system) highly increases at the transition point. This means that such subsystems can be strongly correlated even if they are separated by a large distance. The main goal of the present work is the study of quantum correlations, specifically the entanglement and the local quantum uncertainty (LQU), in systems presenting one or more quantum phase transitions. Specifically, we consider three models of spin chains: 1) The XY and the XY T, which describes chains of spins- 1=2 —the second considering three spins interaction while the first one takes into account only pairwise interactions; 2) A model describing a chain formed by bosonic spins, i.e. particles with spin-1. As a general conclusion, quantum correlation provides a very powerful tool for the study of critical phenomena, providing, among other things, a means to identify a quantum phase transition.As correlações são onipresentes na natureza e têm desempenhado um papel extremamente importante na vida humana por um longo tempo. Por exemplo, na economia correlações entre oferta e demanda são extremamente importantes para um homem de negócios (ou mesmo para um governo) tomar decisões à respeito de sua política de investimento. No campo da biologia, correlações genéticas são fundamentais para seguirmos características individuais. A relação entre distribuição de renda e taxa de criminalidade é apenas um dos exemplo vindos das Ciências Sociais. De um modo geral, a correlação é uma quantidade que descreve o grau de relação entre duas variáveis. No domínio clássico, essa quantidade pode ser medida no âmbito da teoria da informação, desenvolvida por Shannon em 1948. Focando no assunto do presente trabalho, a discussão sobre a natureza quântica das correlações permeia a física desde que Einstein, Podolski e Rosen publicaram seu famoso artigo criticando a mecânica quântica. Desde então, as chamadas correlações quânticas têm se mostrado uma ferramenta muito importante no estudo da Física de muitos corpos. Outra característica da Física de muitos corpos é que certos sistemas, em certas condições, exibem o que chamamos de transição de fase quântica. Tais transições são análogas às transições clássicas, mas sendo governadas por flutuações de natureza puramente quântica, podendo ocorrer à temperatura zero, ao contrário das primeiras, que são guiadas por flutuações térmicas. Um dos principais fenômenos que caracterizam estas transições é o fato de que o comprimento de correlação (definido entre dois subsistemas do sistema global) torna-se de longo alcance no ponto de transição. Isso significa que tais subsistemas podem estar fortemente correlacionados mesmo estando separados por uma grande distância. O objetivo deste trabalho é o estudo de correlações quânticas, mais especificamente do emaranhamento e da incerteza local quântica (LQU), em cadeias de spin que apresentem uma ou mais transições quânticas de fase. Especificamente, estudamos três modelos de cadeias de spin: Os modelos XY e XY T, que são cadeias formadas por spins-1=2, sendo que o segundo considera interação entre três spins enquanto o primeiro somente entre pares; um modelo formado por partículas bosônicas de spin-1. Como conclusão geral, temos que as correlações quânticas fornecem uma ferramenta muito boa para o estudo de fenômenos críticos, oferecendo, entre outros, um meio de identificarmos uma transição quântica de fase.Submitted by Cláudia Bueno (claudiamoura18@gmail.com) on 2015-12-03T14:15:36Z No. of bitstreams: 2 Dissertação - Andesson Brito Nascimento - 2015.pdf: 4640566 bytes, checksum: dbcca8bfca43a95c51641cfa230b0285 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-12-04T06:59:29Z (GMT) No. of bitstreams: 2 Dissertação - Andesson Brito Nascimento - 2015.pdf: 4640566 bytes, checksum: dbcca8bfca43a95c51641cfa230b0285 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Made available in DSpace on 2015-12-04T06:59:29Z (GMT). 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dc.title.por.fl_str_mv |
Correlações quânticas em sistemas críticos |
dc.title.alternative.eng.fl_str_mv |
Quantum correlations in critical systems |
title |
Correlações quânticas em sistemas críticos |
spellingShingle |
Correlações quânticas em sistemas críticos Nascimento , Andesson Brito Correlações quânticas Sistemas críticos Cadeia de spin Quantum correlations Critical systems Spin chain CIENCIAS EXATAS E DA TERRA::FISICA |
title_short |
Correlações quânticas em sistemas críticos |
title_full |
Correlações quânticas em sistemas críticos |
title_fullStr |
Correlações quânticas em sistemas críticos |
title_full_unstemmed |
Correlações quânticas em sistemas críticos |
title_sort |
Correlações quânticas em sistemas críticos |
author |
Nascimento , Andesson Brito |
author_facet |
Nascimento , Andesson Brito |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Céleri , Lucas Chibebe |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/6630683190018665 |
dc.contributor.referee1.fl_str_mv |
Céleri, Lucas Chibebe |
dc.contributor.referee2.fl_str_mv |
Almeida, Agnaldo Rosa de |
dc.contributor.referee3.fl_str_mv |
Almeida, Norton Gomes de |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/2627207807532627 |
dc.contributor.author.fl_str_mv |
Nascimento , Andesson Brito |
contributor_str_mv |
Céleri , Lucas Chibebe Céleri, Lucas Chibebe Almeida, Agnaldo Rosa de Almeida, Norton Gomes de |
dc.subject.por.fl_str_mv |
Correlações quânticas Sistemas críticos Cadeia de spin |
topic |
Correlações quânticas Sistemas críticos Cadeia de spin Quantum correlations Critical systems Spin chain CIENCIAS EXATAS E DA TERRA::FISICA |
dc.subject.eng.fl_str_mv |
Quantum correlations Critical systems Spin chain |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::FISICA |
description |
Correlations are ubiquitous in nature and have played an extremely important role in human life for a long time. For example, in economy, correlations between price and demand are extremely important for a businessman (or even a government) to make decisions regarding their investment policy. In the field of biology, genetic correlations are central to follow individual characteristics. The relationship between income distribution and crime rate is just one example coming from the social sciences. Mathematically, correlation is a number that describes the degree of relationship between two variables. In the classical domain, this number can be computed in the context of information theory, developed by Shannon in 1948. Focusing on the subject of the present work, the discussion regarding the quantum nature of the correlations permeates physics since Einstein, Podolski and Rosen published their famous article criticizing quantum mechanics. Since then, the so-called quantum correlations have been shown to be a very important tool in the study of many-bodies physics. Another feature of many-body physics is that certain systems, under certain conditions, exhibit what we call quantum phase transition. Such transitions are analogous to the classical transitions, but being governed by purely quantum fluctuations and, as such, may occur at zero temperature, unlike the former, which are guided by thermal fluctuations. One of the main phenomenon that characterizes these transitions is the fact that the correlation length (defined between two subsystems of the global system) highly increases at the transition point. This means that such subsystems can be strongly correlated even if they are separated by a large distance. The main goal of the present work is the study of quantum correlations, specifically the entanglement and the local quantum uncertainty (LQU), in systems presenting one or more quantum phase transitions. Specifically, we consider three models of spin chains: 1) The XY and the XY T, which describes chains of spins- 1=2 —the second considering three spins interaction while the first one takes into account only pairwise interactions; 2) A model describing a chain formed by bosonic spins, i.e. particles with spin-1. As a general conclusion, quantum correlation provides a very powerful tool for the study of critical phenomena, providing, among other things, a means to identify a quantum phase transition. |
publishDate |
2015 |
dc.date.accessioned.fl_str_mv |
2015-12-04T06:59:29Z |
dc.date.issued.fl_str_mv |
2015-07-24 |
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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publishedVersion |
dc.identifier.citation.fl_str_mv |
NASCIMENTO, A. B. Correlações quânticas em sistemas críticos. 2015. 90 f. Dissertação (Mestrado em Física) - Universidade Federal de Goiás, Goiânia, 2015. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/4991 |
identifier_str_mv |
NASCIMENTO, A. B. Correlações quânticas em sistemas críticos. 2015. 90 f. Dissertação (Mestrado em Física) - Universidade Federal de Goiás, Goiânia, 2015. |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/4991 |
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por |
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3162138865744262028 |
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600 600 600 600 |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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UFG |
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Brasil |
dc.publisher.department.fl_str_mv |
Instituto de Física - IF (RG) |
publisher.none.fl_str_mv |
Universidade Federal de Goiás |
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