http://www.bdtd.uerj.br/handle/1/3685 2026-03-17T06:36:34Z http://www.bdtd.uerj.br/handle/1/25219 Título: Equações de movimento e transporte semiclássico em sistemas topológicos Autor: Santos, Guilherme Rafael Ferreira dos Primeiro orientador: Barci, Daniel Gustavo Abstract: This work aims to investigate how topology contributes to electronic transport in the presence of a external electromagnetic field. To this end, the evolution of transport models is presented, starting with the classical Drude model, followed by the Sommerfeld model, and subsequently the description of solids through a crystal lattice subjected to a periodic potential. Considering the time-dependent Schrödinger equation, the adiabatic approximation is employed, yielding both the dynamic phase and the geometric Berry phase. It is through the Berry phase that the Berry curvature is determined in the semiclassical equations. From this, the wave packet for the semiclassical regime is constructed, and through the application of the Euler–Lagrange equation to the semiclassical Lagrangian, the semiclassical equations with topology are deduced. These expressions make it possible to describe the Hall effect and to analyze the contribution of the topological magnetic field to electronic transport. Finally, the formalism is applied to the Su–Schrieffer–Heeger (SSH) model, which describes a one-dimensional topological insulator, showing how the band structure and the Berry phase manifest, giving rise to a system with nontrivial topology. Thus, the work provides a conceptual foundation for the introduction of topology in the study of electronic dynamics in solids. Instituição: Universidade do Estado do Rio de Janeiro Tipo do documento: Dissertação 2025-08-28T00:00:00Z http://www.bdtd.uerj.br/handle/1/24785 Título: Paredes de domínio planas na relatividade geral e nas teorias híbridas da gravitação Autor: Silva, Ruan Teixeira da Primeiro orientador: Perez Bergliaffa, Santiago Esteban Abstract: In this work we describe flat domain walls using general relativity and hybrid theories of gravitation that combine the metric and Palatini formalisms. We also analyze these bodies in Minkowski spacetime. The scalar-tensor representation of the hybrid theories is used to facilitate the mathematical calculations. The field equations for the hybrid case were transformed into a single second-order nonlinear differential equation, whose unknowns are three functions that depend on the same variable. These functions are the potential, the scalar field and the metric coefficient. To obtain an equation with one unknown, we imposed two of these functions. This was done twice by imposing distinct pairs and in each case we analyzed the resulting differential equation at points very far from the domain wall and at points very close to the origin. Instituição: Universidade do Estado do Rio de Janeiro Tipo do documento: Dissertação 2025-07-30T00:00:00Z http://www.bdtd.uerj.br/handle/1/24776 Título: Efeitos das interações elétron-elétron na supercondutividade convencional Autor: Vale, Guilherme da Silva do Primeiro orientador: Barci, Daniel Gustavo Abstract: Seeking to contribute to the understanding of the superconductivity phenomenon, we investigate the effects that electron-electron interactions can have on the superconducting phase. We describe the BCS theory of John Bardeen, Leon Cooper, and John Robert Schrieffer, which is used to describe conventional superconductors where superconductivity occurs due to electron-electron coupling caused by phonon sin the lattice of the superconducting material. However, materials that are not described by this theory have attracted much interest since the 1980s, not only because they challenge a well-established theory but also because they exhibit important characteristics, such as the conducting phase at high temperatures. We propose an approach where we construct a model by adding a Fermi liquid-type interaction term to the BCS Hamiltonian. With this, we obtain the self-consistent equations for this model and write a computer program capable of solving them. As a result, we obtain graphs that represent the effects of the Fermi liquid term on the superconducting order parameters. We then point out that this term affects the Fermi surface of the system, potentially deforming it, and that this added term is capable of inducing superconducting phases with different symmetries coexisting. Instituição: Universidade do Estado do Rio de Janeiro Tipo do documento: Dissertação 2025-01-14T00:00:00Z http://www.bdtd.uerj.br/handle/1/24611 Título: Grupo de renormalização variacional: uma abordagem para o potencial efetivo à temperatura finita de uma teoria escalar Autor: Câmara, Lucas Gondim Primeiro orientador: Ramos, Rudnei de Oliveira Abstract: This work investigates the issues of scale dependence present in thermal resummation approaches, such as those produced by the Optimized Perturbation Theory (OPT). To address this challenge, this work proposes a prescription that enhances the effective potential of OPT through a methodology called Renormalization Group Improvement (RGI). This approach modifies the effective potential of the theory by including new terms that ensure renormalization group invariance, thereby significantly reducing scale dependence without altering the standard procedures of OPT. The application of the RGI methodology in the context of OPT, leading to what we call Variational Renormalization Group (VRG), when applied to the finite temperature λϕ4 model, produced promising results in reducing the scale dependence in different thermodynamic quantities. In the symmetric phase, a notable reduction in scale dependence was observed for values of the coupling (λ > 1). In the broken phase, for large values of coupling and field, the VRG effectively mitigated the scale dependence while preserving the second-order phase transition universality class of the λϕ4 model. For small couplings, the results obtained by the VRG resemble those of the OPT, with a slight advantage observed for the OPT. Instituição: Universidade do Estado do Rio de Janeiro Tipo do documento: Tese 2025-06-03T00:00:00Z