Tópicos em defeitos deformados e o movimento Browniano

• Autor(a) principal: Santos, Joao Rafael Lucio dos
• Data de Publicação: 2013
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/tede/5748
• topic: Teoria Clássica de Campos; Campos Escalares; Soluções Analíticas; Kinks; Lumps; Potenciais; Movimento Browniano; Equação de Langevin; Integrais de Trajetória; Classical Field Theory; Scalar Fields; Analytical Solutions; Kinks; Lumps; Potentials; Brownian Motion; Langevin Equation; Path Integral; CIENCIAS EXATAS E DA TERRA::FISICA

The non-linear science is a central topic covering several investigation areas, such as biology, chemistry, mathematics and physics. In the first part of this thesis, we studied the non-linearity in the scope of classical field theory. The discussions are based on static solutions in (1, 1) space-time dimensions, and they are focused on kinks and lumps defects. In the related procedures, we show several techniques which allowed us to determine new models with their respective analytical solutions. The main mathematical tool to obtain these results is the so called deformation method, which was also an essential piece in the construction of a new extension method. This method presents the determination of new two scalar fields models from the coupling between two one scalar field systems. The method was analyzed carefully, as well as the linear stability, the zero modes, the total energy and the superpotentials, related with the new families of potentials. Furthermore, in the second part we presented the basics concepts about the Brownian Motion, where we analised the features of the solution of the Langevin Equation, and we also introduced a path integral approach to this problem in a quantum field theory way.