Dinâmica de defeitos topológicos em modelos hiperbólicos generalizados

Abstract

In this work, we take real scalar fields to study the collision process of solutions like kink. We carried out a literature review, obtaining the characteristics and performing collisions of the soliton-type solutions of the integrable sine-Gordon model and the non-integrable models φ 4 and φ 6 . Collisions point to the influence of vibrational modes on the scattering process. We present a family of generalizations of hyperbolic models, working with a generating function of hyperbolic potentials. We consider two theories generated by this generating function to study scattering, which we call the H4 model and the H6 model. In the H4 theory the phenomena resulting from the collision process are diversified, being states of bion, resonance windows, suppression and reappearance of two-bounce windows, creation of oscillating pulses and variation of the critical speed with a parameter characteristic of the theory. The richness of phenomena was also present in the interactions of the solutions of the model H6

. In the configuration kink-antikink, we found states of bion and phenomena of one-bounce characterized by an initial topological sector change, in which the solutions are inserted, windows of one-bounce, visits to the secondary topological sector, three-bounce, creation of oscillating pulses and a pattern for the pair decay of solutions into oscillating pulses. In the configuration antikink-kink, we found states of bion, resonance windows, suppression of two-bounce windows, a same two-bounce window leading to different order collisions and the creation of oscillating pulses.