Fases Geométricas e suas relações com a Teoria de Fibrados e Representação de Grupos.
We present the own mathematic formalism to, first of all, study the holonomy interpretations of the adiabatic geometric phase presented by Berry-Simon and Aharanov-Anadan and, after this, the similirities found with the theory of representation groups, particularly, with the Borel-Weil-Bott theorem....
| Autor: | |
|---|---|
| Tipo de recurso: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2008 |
| País: | Brasil |
| Institución: | Universidade Federal da Paraíba (UFPB) |
| Repositorio: | Biblioteca Digital de Teses e Dissertações da UFPB |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufpb.br:tede/7394 |
| Acceso en línea: | https://repositorio.ufpb.br/jspui/handle/tede/7394 |
| Access Level: | acceso abierto |
| Palabra clave: | Matemática Fibrado linha Holonomia Berry s phase Adiabatic phase Line Bundle Homolonomy Nonadiabatic phase CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| Sumario: | We present the own mathematic formalism to, first of all, study the holonomy interpretations of the adiabatic geometric phase presented by Berry-Simon and Aharanov-Anadan and, after this, the similirities found with the theory of representation groups, particularly, with the Borel-Weil-Bott theorem. These relations are made through classification of complex bundle line, and these results are used to introduce a cranked Hamiltonian. In general, we also show that the parameter space is a flag manifold or a submanifold of her and present a topologic argument of this space that indicates the relation between the structure Riemannian and the Berry s connection. |
|---|