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DC Field | Value | Language |
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dc.contributor.advisor1 | Andrade, Fabiano Manoel de | - |
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dc.contributor.referee1 | Castro, Antônio Sérgio Magalhães de | - |
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dc.contributor.referee2 | Schmidt, Alexandre | - |
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dc.contributor.referee3 | Bazeia, Dionisio | - |
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dc.contributor.referee4 | Batista, Antonio Marcos | - |
dc.contributor.referee4Lattes | http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4705323T1&tokenCaptchar=03ANYolqsE2VNpILr--pPGBZKGZFLEfjr_C54fEg6c075pZGWaWJF8Ce2c1dLpSCyJBrn0pP4sdSqK4aqgSLvOJhocQNGRF2fhTH-B598Vo-ZvUM01VwyzKsmnw0PPeOOOOnWIQ_zXBEy4GQN4ghOemzCzb3IvJXF8BGMQ4w_SPW5CUh5JpaQsrQ3GxS-Ufdom5YIaS3Zj3JsnBcVvM4kq8_UyfeKkEFo53casOMVIwTmsODEGyk1uf5ddtP5T_myvSgElQoqSFBNoIYcX9rTEzKfM_KLpeR6WaK75UWKGQtI3LqdeWK0abild6CMznwOL9nD7CIZuy0WG-7QZPSJjn6sinwaSYf7jvpTx1YamMF4WmRjCFsUU9YQ_ce8WAeqgH_S_dL-sMmWUdCDSQvE8eIFxQ4EWdGLVtLqZxt4if9U1wz8s3AJvVzTDDeWhFLE7ztzy_IBt4yQvG6OPU1uAOu7nT591Ulsi0DvV_xs-OVhCdPZ_OM8smixMfdbU_W5nbtJmpTXwq2yDYrp29XNGGV7DSqwMpZyN0Q | pt_BR |
dc.creator | Uhdre, Gustavo Mehanna | - |
dc.creator.Lattes | http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4362478J3&tokenCaptchar=03ANYolqutKLj7wmRlptl36qVTg2qLusrR40mr_0sBhQEiDSndWhvUag5l5kG-EYA771ePLYtEYugPF25FZBCQ7E0t8U3x8oLP5tY-GfqWwE6LsbSNOlPmKpS_T8LTeYFRQxUt_eKuf8U0DtdVYDejB-G0PhCuT0slhHehHq9BP1jmIlJ9MKkQOtnaKmywiYy5AVXLRHckhmi-PWtmShLk6TAGx0TVjhmh7_eBQRriNS3BPz4qOTuB1owSjW89pppRTGVwT6qaQA_Qix0LkUBJt3iQZkDogKb908wgLj-geHDmI9tw2WayVf8ZiMtMnCD-uMJRBK8nq8SW1-a-AVNL6S8NCy62eN4wlgXpnqkrjQV5fV6H0Gwyn2Rw74wf42fSYggtuOhL7nYhv7pIJgrwftJzbz_eqns4QcieRHOBNfUPc8_bE9WCPwaRJIvXPoqU-KQvJTkVLIlzG_2ZniejgnUfBCzr0xJNiLpmGOr6QUNxkDnNtxHUHtxOLA1gjSA0agq1M581ITEkMmjr_t1Uv34G5jeGi_EWUw | pt_BR |
dc.date.accessioned | 2022-07-19T22:02:05Z | - |
dc.date.available | 2022-07-19 | - |
dc.date.available | 2022-07-19T22:02:05Z | - |
dc.date.issued | 2022-04-04 | - |
dc.identifier.citation | UHDRE, Gustavo Mehanna. Deformações quânticas de sistemas relativísticos e suas conexões com sistemas ópticos. 2022. Tese (Doutorado em Ciência Física) - Universidade Estadual de Ponta Grossa. Ponta Grossa. 2022. | pt_BR |
dc.identifier.uri | http://tede2.uepg.br/jspui/handle/prefix/3671 | - |
dc.description.abstract | In this thesis, we aim to analyze the effects of quantum deformation on the dynamics of collapses and revivals of the spin inversion of an optical system. This deformation occurs in the structures of spacetime, called the κ-deformation. To carry out this analysis, we will map the Hamiltonian of the κ-deformed Dirac oscillator onto the Jaynes-Cummings Hamiltonian. Firstly, we show how to map the Dirac oscillator in (2+1) dimensions in the Jaynes-Cummings and anti-Jaynes-Cummings system simultaneously, without the deformation. We show that using a suitable basis of Dirac matrices to write the system in (2+1) dimensions, we find a chirality symmetry of the system. From this, we use the κ-deformed Dirac equation obtained from the κ-deformed Poincar ́e generators to write the Hamiltonian of the κ-deformed Dirac oscillator. We show that the Hamiltonian of the κ- deformed Dirac oscillator is non-Hermitian, but its eigenvalues are real, which characterizes the Hamiltonian as being quasi-Hermitian. Since the Hamiltonian of the κ-deformed Dirac oscillator is quasi-Hermitian, we can apply a similarity transformation, called Dyson map, which allows us to obtain its Hermitian counterpart, leaving its eigenvalues and expected values invariant. Finally, we show that the deformation adds new entangled states to the system which causes a change in the frequency of Zitterbewegung and, as a consequence of this, the collapses and revivals of the spin inversion of system are also affected. We also show that the total angular momentum in the z direction is not conserved anymore, as a direct consequence of the deformation. | pt_BR |
dc.description.resumo | Nesta tese, temos por objetivo analisar os efeitos da deforma ̧c ̃ao quˆantica na dinˆamica de colapsos e ressurgimentos da invers ̃ao de spin de um sistema ́optico. Essa deforma ̧c ̃ao ocorre nas estruturas do espa ̧co-tempo, chamada de deforma ̧c ̃ao κ. Para realizar esta an ́alise, fare- mos um mapeamento do Hamiltoniano do oscilador de Dirac κ-deformado no Hamiltoniano de Jaynes-Cummings. Primeiramente, mostramos como fazer o mapeamento do oscilador de Dirac em (2+1) dimens ̃oes no sistema de Jaynes-Cummings e anti-Jaynes-Cummings simultaneamente, sem a deforma ̧c ̃ao. Mostramos que usando uma base adequada das matrizes de Dirac para escrever o sistema em (2+1) dimens ̃oes, encontramos uma simetria de quiralidade do sistema. A partir disso, usamos a equa ̧c ̃ao de Dirac κ-deformada obtidas dos geradores de Poincar ́e κ-deformado para escrever o Hamiltoniano do oscilador de Dirac κ-deformado. Mostramos que o Hamiltoniano do oscilador de Dirac κ-deformado ́e n ̃ao hermitiano, por ́em seus autovalores s ̃ao reais, o que caracteriza o Hamiltoniano como sendo quase hermitiano. Sendo o Hamiltoniano do oscilador de Dirac κ-deformado quase hermitiano, podemos aplicar uma transforma ̧c ̃ao de similaridade, chamada mapa de Dyson, o qual nos permite obter sua contrapartida hermitiana, deixando invariante os seus autovalores e valores esperados. Por fim, mostramos que a deforma ̧c ̃ao adiciona novos estados emaranhados ao sistema o que causa uma modifica ̧c ̃ao na frequˆencia de Zitterbewegung e, como consequˆencia disso os colapsos e ressurgimentos da invers ̃ao de spin sistema tamb ́em s ̃ao afetados. Mostramos tamb ́em que o momento angular total do sistema na dire ̧c ̃ao z n ̃ao ́e conservado devido `a presen ̧ca da deforma ̧c ̃ao. | pt_BR |
dc.description.provenance | Submitted by arlindo kohlrausch (ajfk@uepg.br) on 2022-07-19T22:02:05Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Gustavo Mehanna Uhdre.pdf: 2655716 bytes, checksum: 01ad3bffac66a7ce45e2315ff87496d5 (MD5) | en |
dc.description.provenance | Made available in DSpace on 2022-07-19T22:02:05Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Gustavo Mehanna Uhdre.pdf: 2655716 bytes, checksum: 01ad3bffac66a7ce45e2315ff87496d5 (MD5) Previous issue date: 2022-04-04 | en |
dc.description.sponsorship | Coordenação de Aperfeiçoamento de Pessoal de Nível Superior | pt_BR |
dc.language | por | pt_BR |
dc.publisher | Universidade Estadual de Ponta Grossa | pt_BR |
dc.publisher.country | Brasil | pt_BR |
dc.publisher.department | Departamento de Física | pt_BR |
dc.publisher.program | Programa de Pós-Graduação em Ciências | pt_BR |
dc.publisher.initials | UEPG | pt_BR |
dc.rights | Acesso Aberto | pt_BR |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Brazil | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/br/ | * |
dc.subject | Oscilador de Dirac | pt_BR |
dc.subject | Algebra κ-Poincare-Hopf | pt_BR |
dc.subject | Sistema Jaynes-Cummings | pt_BR |
dc.subject | Dirac oscillator | pt_BR |
dc.subject | κ-Poincare-Hopf algebra | pt_BR |
dc.subject | Jaynes-Cummings System | pt_BR |
dc.subject.cnpq | CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA | pt_BR |
dc.title | Deformações quânticas de sistemas relativísticos e suas conexões com sistemas ópticos. | pt_BR |
dc.type | Tese | pt_BR |
dc.contributor.instituicao-banca1 | Universidade Estadual de Ponta Grossa | pt_BR |
dc.contributor.instituicao-banca2 | Universidade Federal Fluminense | pt_BR |
dc.contributor.instituicao-banca3 | Universidade Federal da Paraíba | pt_BR |
dc.contributor.instituicao-banca4 | Universidade Estadual de Ponta Grossa | pt_BR |
Appears in Collections: | Programa de Pós - Graduação em Ciências |
Files in This Item:
File | Description | Size | Format | |
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Gustavo Mehanna Uhdre.pdf | tese completa em pdf | 2.59 MB | Adobe PDF | View/Open |
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