Um estudo sobre a fase geométrica de Berry e o efeito Aharonov-Bohm dual

• Autor(a) principal: Favarato, Cássio Cecato
• Data de Publicação: 2014
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Federal do Espírito Santo (riUfes)
• Texto Completo: http://repositorio.ufes.br/handle/10/7457
• topic: Berry’s geometric phase; Adiabatic approximation; Gauge fields; Dual aharonov-Bohm effect; Berry’s geometric phase; Dual Aharonov-Bohm effect; Fase geométrica de Berry; Aproximação adiabática; Campos de calibre; Efeito Aharonov-Bohm dua; Física; Campos de calibre (Física); 53

In this work, we make a review of the literature that the so-called Berry’s geometric phase. A recent issue, which has been employed in various areas of physics. For this, we use, in a number of references, in which many were critical to the theoretical foundation of this work. At first, we focus on the study of the time evolution of quantum systems governed by Hamiltonians operators whose time dependence is manifested by a set of parameters called classical fields. The adiabatic approximation, is justified mathematically when demonstrated the adiabatic theorem. Under these conditions, we obtain geometric phases - Berry’s phase - associated with these systems in different representations, each displaying its particularity. Finally, as a particular case of geometric phase, we studi from the viewpoint of duality transformations of Maxwell’s equations, the dual Aharonov-Bohm effect, extracting the geometric Berry’s phase associated with the dynamics of the magnetic monopole in the presence of the electric vector potential