Análise de espalhamento de defeitos topológicos e não topológicos em (1,1) dimensões

Abstract

In this thesis, we study the collision process for solutions of nonlinear scalar field theories in (1, 1) dimensions. We reproduce the main results following a timeline of papers about kink collisions for the sine-Gordon, φ 4 , and φ 6 models. Moreover, we describe the role of the internal modes in the collision process via the energy exchange mechanism. Next, we study the boundary scattering on the half-line with a Neumann-type boundary condition for both φ 4 and φ 6 models. The scattering on the half-line exhibits sensible modifications in the dynamics compared with the scattering on the line. On the half-line, the outputs depend on the initial velocity and the boundary. In particular, for both models, the resonance window structures are modified by the boundary effects with the restoration of missing windows. In the following, we present the results of collisions for large and small kink-antikink of a double sine-Gordon model depending on only one parameter r. For some parameter intervals we observe two connected effects: the production of multiple antikink-kink pairs and up to three solitary oscillations. The scattering process for small kink-antikink has several possibilities: the change of the topological sector, one-bounce collision, two-bounce collision, or formation of a bion state. In particular, we observed for small values of r and velocities, the formation of false two-bounce windows and the suppression of true two-bounce windows, despite the presence of an internal shape mode. We also study collisions of lump solutions in a model with a false vacuum depending on a parameter s. The model has unstable nontopological lump solutions with a bell shape for small s, acquiring a flat plateau around the maximum for large s. For s → ∞ the φ 4 model is recovered. We show that for s ≳ 2 the lump is metastable with the only negative mode very close to zero. Metastable lumps can propagate and survive long enough to produce dynamical effects. We find that the lump-lump collision can result in one or two kink-antikink pairs, bion states, and some regularly traveling oscillations.