Estudo de colisões de paredes de Bloch e localização de modos ferminônicos

Abstract

In this work we numerically study the collision process of domain-walls in a system with two coupled scalar fields, which generates a wall with internal structures, the so called Bloch Walls. If the initial velocity is less than 0, 57... occurs inelastic scattering and part of the energy is lost as radiation. We realize that the objects resulting from the collision belong to a topological sector which is different from those chosen in the beginning of the process. In other words, the system transit from a sector AA-like to a sector AB-like one. The reflected solitary waves have approximately half of the initial energy. Besides of the decay of the sector AA to AB one, we note that part of the energy is converted into a coherent structure which oscillates in the center of the net, with approximately half of the initial energy of the system. We have studied also bound states of the system in the case of two walls which initially are close and with null velocity. The resulting structure lose energy as radiation. However, the energy loss is gradual, like in the case of the breathers of the Á4 model. On the other hand, we have studied the coupling of fermions to the Bloch domainwall. The coupling between the fermionic field and two different scalar fields named Á and  it is a Yukawa-type coupling. We have showed that the fermionic zero mode is localized at x = 0 in the scalar field Â, which means that the ferminonic field is localized inside wall. The fermionic mass in the vacuum sector is the same obtained for the Á4 model, since that the mass of the scalar field  in the vacuum sector is zero.