Sobre defeitos, twistons e férmions.

Abstract

Topological defects are solutions of differential equations that connect distinct confi gurations of a system. For one-dimensional models these solutions are called kinks. In this work we will study the twist-like solutions, called topological twistons and also investigate the behavior of fermions in the presence of kink-like structures. First we will study the topological twistons present in the crystalline polyethylene which represent a 180 twist in the CH2 chain also causing a contraction of the length of the molecule. We intend to construct an effective model of two elds that does not contain degeneracy in the energy through the application of the so called Extension Method, also seeking to obtain analytical solutions of this model. After this study, we will turn our investigations for fermion analyzes in the presence of kinks in order to control of the threshold energy (energy gap where bound states reside) using two scalar elds.