Defeitos topológicos e cadeias cíclicas de deformação aplicados em diferentes cenários

Abstract

In order to obtain structures known as defects, it was used a systematic procedure which holds cyclic deformation chains. This cyclical procedure enables that the initial defect (used to trigger the chain) is recovered via the process of successive deformations. This technique was applied considering topological kink like defects derived from two models, 4 and sine-Gordon, described by a single real scalar eld. The results show that this procedure can generate simultaneously kink and lump like defects with topological mass satisfying closed relations. After the detailed description and analysis of this method, some of its results were applied in brane scenario, where we studied the quantum problem analogue derived from a metric perturbation. The scenarios includes thick branes results that could support 4-dimensional gravity inside. Finally, we studied the topological origin of vacuum transitions in scenarios supported by double-well potentials. It was found that the Wigner function, constructed by means of the ground and rst excited states (solutions of the normal modes potential spectrum), performs quantum tunneling moving from one minimum to another in the potential. The tunneling analysis was performed by a prescription of the Wigner's function dynamics and the time dependence of stagnation points for an analytical double well potential.