Estudo comparativo entre duas teorias de perturbação dependentes do tempo em mecânica quântica

Detalhes bibliográficos
Ano de defesa: 2016
Autor(a) principal: Lima, Diogo Henrique Garcia
Orientador(a): Rigolin, Gustavo Garcia lattes
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Universidade Federal de São Carlos
Câmpus São Carlos
Programa de Pós-Graduação: Programa de Pós-Graduação em Física - PPGF
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Área do conhecimento CNPq:
Link de acesso: https://repositorio.ufscar.br/handle/20.500.14289/7922
Resumo: This monograph shows two perturbative methods to determine the time evolution of quantum systems described by time-depependent Hamiltonians. One method is the standard time-dependent perturbation theory usually found in text books of quantum mechanics. The other method is the adiabatic perturbation theory, whose perturbative corrections are obtained from the quantum adiabatic approximation. To compare the efficiency of those methods we apply them to two time-dependent problems. One is the Landau- Zener problem, whose time dependency is linear on time. We also show three analytical solutions to this problem. The other problem is a Hamiltonian which has a cyclic perturbation, whose numerical solution is employed to compare the efficacy of both perturbative methods. The comparison between the two perturbation theories is based on the graphics of transition probability and of the fidelity, where all quantities are computed using the perturbative methods and the exact solutions to the problems. We conclude that the adiabatic perturbation theory improves the adiabatic approximation, is better than the standard theory when we deal with the limited Hamiltonian, and is relatively better than the standard theory for the Landau-Zener model.