Fases geométricas, quantização de Landau e computação quâantica holonômica para partículas neutras na presença de defeitos topológicos

• Ano de defesa: 2009
• Autor(a) principal: Bakke Filho, Knut
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraí­ba; BR; Física; Programa de Pós-Graduação em Física; UFPB
• Palavras-chave em Português: Fases geométricas; Defeitos topológicos; Espaço-tempo curvo; Espaço-tempo curvo e com torção; Computação quântica holonômica; Quantização de Landau; Efeito Aharonov-Casher; Efeito He-McKellar-Wilkens; Efeito Mashhoon; Efeito Sagnac; Geometric phases; Topological defects; Curved spacetime; Cuverd spacetime with torsion field; Holonomic quantum computation; Landau quantization; Aharonov- Casher efect; He-McKellar-Wilkens efect; Mashhoon efect; Sagnac efect; Anandan quantum phases; Local reference frame; Fermi-Walker reference frame; Rotating frames; Dirac equation; Foldy-Wouthuyssen approach; Spinors; Graphene; Kaluza-Klein Theory; CIENCIAS EXATAS E DA TERRA::FISICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/5724

We start this work studying the appearance of geometric quantum phases as in the relativistic as in the non-relativistic quantum dynamics of a neutral particle with permanent magnetic and electric dipole moment which interacts with external electric and magnetic fields in the presence of linear topological defects. We describe the linear topological defects using the approach proposed by Katanaev and Volovich, where the topological defects in solids are described by line elements which are solutions of the Einstein's equations in the context of general relativity. We also analyze the in uence of non-inertial effects in the quantum dynamics of a neutral particle using two distinct reference frames for the observers: one is the Fermi-Walker reference frame and another is a rotating frame. As a result, we shall see that the difference between these two reference frames is in the presence/absence of dragging effects of the spacetime which makes its in uence on the phase shift of the wave function of the neutral particle. In the following, we shall use our study of geometric quantum phases to make an application on the Holonomic Quantum Computation, where we shall show a new approach to implement the Holonomic Quantum Computation via the interaction between the dipole moments of the neutral particle and external fields and the presence of linear topological defects. Another applications for the Holonomic Quantum Computation is based in the structure of the topological defects in graphene layers. In the presence of topological defects, a graphene layer shows two distinct phase shifts: one comes from the mix of Fermi points while the other phase shift comes from the topology of the defect. To provide a geometric description for each phase shift in the graphene layer, we use the Kaluza-Klein theory where we establish that the extra dimension describes the Fermi points in the graphene layer. Hence, we can implement the Holonomic Quantum Computation through the possibility to build cones and anticones of graphite in such way we can control the quantum uxes in graphene layers. In the last part of this work, we study the Landau quantization for neutral particles as in the relativistic dynamics and non-relativistic dynamics. In the non-relativistic dynamics, we study the Landau quantization in the presence of topological defects as in an inertial as in a non-inertial reference frame. In the relativistic quantum dynamics, we start our study with the Landau quantization in the Minkowisky considering two different gauge fields. At the end, we study the relativistic Landau quantization for neutral particles in the Cosmic Dislocation spacetime.