| dc.contributor | Andrade, Fabiano Manoel de | |
| dc.contributor | 022.148.469-80 | |
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| dc.contributor | Castro, Antônio Sérgio Magalhães de | |
| dc.contributor | 166.404.658-63 | |
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| dc.contributor | Schmidt, Alexandre | |
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| dc.contributor | Bazeia, Dionisio | |
| dc.contributor | 253.190.510-34 | |
| dc.contributor | http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4783283Z8&tokenCaptchar=03ANYolqvp6GhLgzunso0ToS-Qstcs5ufXZC85D2sdKcdIzVheS_2nIoRLlYxgQk-NEHOPUiW5TMS59-NsJlzsQ0AQikJpV2w3-6ZFBZJX2J4ha9iIh6lEF4lxyaForD3X8OHxTrfsXLel9j2AfjWtGOf8YiWF8HDnD2lxKvu3CCDrhQM3nBRdzGaGEDUyfylDO81iIs5YEDDh9YyWnsBikb34TuSyWQmeglYHmeecRrFyZjpDDfeZLQL-Q4EgOjwGD5ExEJR8NUJNIPaIJX9TGSUA4xTxQfWPJHNwPbJyYNQJE7TIsLMaTjR8NqV_AwekMCLx94iJSpRXZMRkVhupy4PR7YvqI_YEQrXlISts3Fra2kUQO0qMWNe3Ttf7_BUIUmyXyRV9Fh1dDfcovGi4xUzbzQFQglSm-aZ74VbN0m0lu19YCcKKCkMhUY1Ntlm9E1yS_KxqMtmO5ZjrNJSeSWkfJ4eVClC6T4zdqMFUvXbO1D9NytJMFEpDwVK6FDz-R-fs9qLsFXGjUODzKYRdEEH_9DnlcF3OCw | |
| dc.contributor | Batista, Antonio Marcos | |
| dc.contributor | 882.000.519-00 | |
| dc.contributor | 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 | |
| dc.contributor | Universidade Estadual de Ponta Grossa | |
| dc.contributor | Universidade Federal Fluminense | |
| dc.contributor | Universidade Federal da Paraíba | |
| dc.contributor | Universidade Estadual de Ponta Grossa | |
| dc.creator | Uhdre, Gustavo Mehanna | |
| dc.date | 2022-07-19T22:02:05Z | |
| dc.date | 2022-07-19 | |
| dc.date | 2022-07-19T22:02:05Z | |
| dc.date | 2022-04-04 | |
| dc.date.accessioned | 2023-08-31T23:35:25Z | |
| dc.date.available | 2023-08-31T23:35:25Z | |
| dc.identifier | 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. | |
| dc.identifier | http://tede2.uepg.br/jspui/handle/prefix/3671 | |
| dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/8568549 | |
| dc.description | 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. | |
| dc.description | 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. | |
| dc.description | Coordenação de Aperfeiçoamento de Pessoal de Nível Superior | |
| dc.language | por | |
| dc.publisher | Universidade Estadual de Ponta Grossa | |
| dc.publisher | Brasil | |
| dc.publisher | Departamento de Física | |
| dc.publisher | Programa de Pós-Graduação em Ciências | |
| dc.publisher | UEPG | |
| dc.rights | Acesso Aberto | |
| dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Brazil | |
| dc.rights | http://creativecommons.org/licenses/by-nc-nd/3.0/br/ | |
| dc.subject | Oscilador de Dirac | |
| dc.subject | Algebra κ-Poincare-Hopf | |
| dc.subject | Sistema Jaynes-Cummings | |
| dc.subject | Dirac oscillator | |
| dc.subject | κ-Poincare-Hopf algebra | |
| dc.subject | Jaynes-Cummings System | |
| dc.subject | CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA | |
| dc.title | Deformações quânticas de sistemas relativísticos e suas conexões com sistemas ópticos. | |
| dc.type | Tese | |
