Efeitos da violação de simetria de Lorentz sobre o modelo de Kronig-Penney

• Ano de defesa: 2019
• Autor(a) principal: FEITOSA, Marcelo Augusto dos Reis
• Orientador(a): FERREIRA JUNIOR, Manoel Messias
• Banca de defesa: FERREIRA JÚNIOR, Manoel Messias , SCHRECK, Marco , SILVA, Edilberto Oliveira , MORAES, Fernando Jorge Sampaio
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Maranhão
• Programa de Pós-Graduação: PROGRAMA DE PÓS-GRADUAÇÃO EM FÍSICA/CCET
• Departamento: DEPARTAMENTO DE FÍSICA/CCET
• País: Brasil
• Palavras-chave em Português: Violação de Lorentz; Modelo de Kronig-Penney; Bandas de energia.
• Palavras-chave em Inglês: Lorentz Violation; Kronig-Penney Model; Energy Bands.
• Área do conhecimento CNPq: Física
• Link de acesso: https://tedebc.ufma.br/jspui/handle/tede/tede/4431

The breaking of Lorentz symmetry and its possible eects on physical systems has been a topical issue in actual investigations, belonging to a precision program for establishing the limits of this symmetry in nature. These studies are not constrained to the eld theory or high energy systems, since they also involve other areas, like condensed matter physics. In this work we revisit the Kronig-Penney model, rst addressed by means the Schrodinger equation, and second by means of the Dirac equation in its quantum-relativistic version. We revise the nonrelativistic and relativistic Kronig-Penney model, achieving the energy bands relations to both cases. We verify that in the case of relativistic KP model the eects entail in an energy band reduction, if compared to the non-relativistic case. The same happens to gaps but in a less signicant way. In the sequel, we investigate the eects of the Lorentz-violating term, ψb ̄ μγ5γ μψ, belonging to the fermionic sector of the SME of Colladay & Kostelecky, on the Kronig-Penney model. Here, b μ represents the Lorentz-violating backgroud. As an initial step, we obtain the associated free particle spinor solutions of the modied Dirac equation. We use such spinors to develop the KP model with Lorentz violation and achieve the modied band relations. We verify that the procedure become specially simplied for the unidimensional case, p = (0, 0, 0, pz), for the spacelike conguration of the background, b = (0, 0, 0, bz). The energy band relation has the same general structure from that obtained without LV, with the dierence that dimensionless quantity Γ, dened in that work, carries now the dependence on the Lorentz-violating term. It still misses to analyse how the LV terms aects the band energy structure.