Detalhes bibliográficos
| Ano de defesa: |
2021 |
| Autor(a) principal: |
Miranda, Bruno Martins
 |
| Orientador(a): |
Cardoso, Wesley Bueno
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| Banca de defesa: |
Cardoso, Wesley Bueno,
Malbouisson, Jorge Mário Carvalho,
Almeida, Norton Gomes de |
| Tipo de documento: |
Dissertação
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| Tipo de acesso: |
Acesso aberto |
| Idioma: |
por |
| Instituição de defesa: |
Universidade Federal de Goiás
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| Programa de Pós-Graduação: |
Programa de Pós-graduação em Fisica (IF)
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| Departamento: |
Instituto de Física - IF (RMG)
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| País: |
Brasil
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| Palavras-chave em Português: |
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| Palavras-chave em Inglês: |
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| Área do conhecimento CNPq: |
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| Link de acesso: |
http://repositorio.bc.ufg.br/tede/handle/tede/13603
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Resumo: |
Theoretically predicted in 1923-1924 by Bose and Einstein and experimentally obtained only in 1995, the Bose-Einstein condensate became an important laboratory for the investigation of various quantum phenomena, such as the Josepshon oscillations, the study of vortex, use as interferometers, etc. Using mean-field theory to include the effects of the average interaction between particles, in the 1960s, Gross and Pitaevskii obtained an equation capable of describing the dynamics of a diluted gas at a temperature of 0 K. Dimensional reduction models for the Gross-Pitaevskii equation were developed for several types of confining potentials in order to simplify numerical calculations and reproduce accurate results. For condensates with a strong attractive strength, confined by doublewell potentials, it is known that the phenomenon of spontaneous symmetry breaking occurs. In this state, the particle population between wells becomes asymmetrical, in contrast with the symmetry of the confining potential. In this work, we consider a condensate in the self-focusing regime, confined transversely by a funnel-like potential and axially by a double well formed by the combination of two inverted Pöschl-Teller potentials. We used an effective equation, obtained by means of a variational method for the Gross-Pitaevskii equation, to analyze the symmetry break of the probability density of the wave function that describes the condensate. This symmetry break was observed for several interaction strength values as a function of the minimum potential well. A quantum phase diagram was obtained, in which it is possible to recognize the three phases of the system: symmetric phase (Josepshon), asymmetric phase (spontaneous symmetry breaking - SSB), and collapsed states, i.e., when the solution becomes singular, which does not represent the physical system, showing a validity limit for the model under consideration. We analyzed our symmetric and asymmetric solutions using the real-time evolution method, in which it was possible to confirm the stability of the results. Finally, a comparison with the cubic nonlinear Schrödinger equation in one dimension and the Gross-Pitaevskii equation in three dimensions is performed for the purpose of analyzing the accuracy of the effective equation used here. |
