Dinâmica quântica de uma partícula livre na superfície de um cone duplo

Detalhes bibliográficos
Ano de defesa: 2014
Autor(a) principal: Gomes, Felipe Azevedo
Orientador(a): Não Informado pela instituição
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Universidade Federal da Paraí­ba
BR
Física
Programa de Pós-Graduação em Física
UFPB
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/5755
Resumo: The surfaces physics has attracted the attention of many researchers due to the discovery of materials that exhibit amazing properties and promising technological applications, such as graphene and topological insulators. The study of these new materials has been done considering the Dirac equation for effective models. Within this context, many efforts has been done in the study of the influence the geometric shape of these materials in their physical properties. One of the geometric shapes of interest are the conical surfaces. Interesting effects arise when particles are confined to surfaces of double cones. In this work, we present a brief review of the general Dirac equation and its generalizations to curved spaces and problems with external fields. As studies on graphene had a strong motivation for our work and considering the possibility of extending our results to these problems, we present a brief discussion of the modeling of graphene using the Dirac equation. Then, we review the classical and quantum behavior of a particle on the surface of a double cone [23]. Using the Hamilton formalism, we show that, classically, the movement of a particle with non-zero angular momentum is confined to one of the cones, characterized instability in the solutions with near zero angular momentum. Similar characteristics of instability are also noted in the quantum case. As results, we present a study of quantum-relativistic dynamics of a free particle, and a particle in the presence of a magnetic field azimuthal symmetry, both on the surface of a double cone. We evaluate the existence of instability in case of a free particle and found, in the problem with presence of a magnetic field, distinct energy levels for each cone. In this case, the cones work like independent systems