Efeito Hartman e mecânica bohmiana

• Ano de defesa: 2024
• Autor(a) principal: López, Said José Lantigua
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• dARK ID: ark:/26339/001300001b2vt
• Idioma: por
• Instituição de defesa: Universidade Federal de Santa Maria; Brasil; Física; UFSM; Programa de Pós-Graduação em Física; Centro de Ciências Naturais e Exatas
• Palavras-chave em Português: Efeito Hartman; Geometro-dinâmica; Mecânica bohmiana; Tempo de tunelamento; Hartman effect; Geometro-dynamics; Bohmian mechanics; Tunneling time; CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA
• Link de acesso: http://repositorio.ufsm.br/handle/1/33323

In this work, we present a study of the intriguing Hartman Effect, through two approaches. The first one is a relativistic approach of quantum theory using the Dirac equation, and the second one is a geometrodynamic approach using Bohmian mechanics. Therefore, we first developed a mathematical model from the Dirac equation in an alternative representation, which allowed us to deduce a group (or tunneling) time as the sum of the residence times inside the potential barrier for particles with spin up and spin down, and the self-interaction time between the incident and reflected wave functions of the spin-up particles. In other words, we obtained a model that allows us to observe the influence of spin on the tunneling time, in the absence of an external magnetic field, which offers a less satisfactory explanation of the Hartman Effect in terms of group time. Subsequently, through a geometrodynamic approach of Bohmian mechanics, we constructed a general solution for the problem of scattering of incident particles on a constant potential barrier under the hypothesis that such particles undergo quantum tunneling along geodesic trajectories in an Alcubierre-type spacetime. Consequently, from the solution, we determined the mathematical expressions for the quantum potential, momentum, position, and tunneling time in terms of the spacetime geometry. That is, we obtained a mathematical model that allows us to explain the Hartman Effect as a consequence of the spacetime distortion generated by the quantum potential inside the barrier.