Modelo modificado de toda acoplado a férmion e dualidade sóliton : férmion de Majorana

Abstract

In this doctoral thesis, we present the modified Toda Coupled to Fermion model and the Majorana soliton-fermion duality, with some symmetries being exhibited for both the model, as well as for the equations of motion. We present an expression explicit for the term E, which represents the energy of the Thirring sector of the model, was found a gap in the energy sector where we can locate the bound states of the fermion (Threshold, Majorana) and the BIC bound states that are outside this gap. O multifrequency potential was studied to obtain the real model vacuums that serve to interpolate two soliton solutions from the model. We look for analytical solutions (solitons of the kinks type and bound states of the fermion) making use of the tau function formulation. Subsequently, the inverse reaction of the fermion on kink is presented, where we can highlight the obtaining of an equation from the double sine-Gordon model and another equation for the fermion model. We present the zero mode bound states and emphasize in Majorana states from zero mode to zero and non-zero potential. We explore the fermion reaction and soliton/particle duality (Majorana). we obtained some results numerical data for the model through the so-called Relaxation Method, this method Iterative consists of finding a solution to the system of equations, starting with a “guessed” solution and looking for the true solution.