Efeitos topológicos devido a uma deslocação em espiral em sistemas quânticos relativísticos e não-relativísticos

• Ano de defesa: 2022
• Autor(a) principal: Maia, Anderson Vinícius Dantas Marques
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba; Brasil; Física; Programa de Pós-Graduação em Física; UFPB
• Palavras-chave em Português: Física; Deslocação em espiral; Efeito Aharonov-Bohm; Níveis de Landau; Quantização relativística de Landau; Quantum revivals; Campo elétrico não uniforme; Ponto de corte; Efeitos de rotação; Soluções analíticas; Equação de Schrödinger; Equação de Dirac; Defeito topológico linear; Physics; Spiral dislocation; Aharonov–Bohm effect; Landau levels; Relativistic Landau quantization; Nonuniform electric field; Cut-off point; Rotating effect; Analytical solutions; Schrödinger equation; Dirac equation; Linear topological defects; CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/123456789/26060

In this work, we analyse the influence of the topological defects, like a spiral dislocation in two different scenarios, firstly a non-relativistic system using the Schrödinger equation for a charged particle subject to a confining potential. Furthermore, two systems with spiral dislocation in the presence of a nonuniform radial electric field, one of them with a topology-induced cut-off point yields eigenvalues of energy which are infinitely degenerated. Besides, we study Landau levels with and without rotation effects for a point charge. Thus, in this first non-relativistic part we show that there are cases where an analog of the Ahanorov-Bohm effect exists for bound states and quantum revivals. Next, we analyse the interaction of a relativistic electron with a uniform magnetic field in spiral dislocation. As well, the behaviour of the Dirac field subject to a hard-wall potential. We also show that both rotation and the topology of the spacetime impose a restriction on the values of the radial coordinate. As results, we demonstrate through the Foldy-Wouthuysen approximation that the non-relativistic limits of these situations are consistent with the solutions obtained in the first part of the thesis.