Aspectos da não linearidade em fenômenos de ressurgimento por uma técnica não perturbativa

Abstract

In the present work we apply a semi-classical non-perturbative technique to study revival times in relevant models. First we use a schematic model that is commonly used to simulate the interatomic interaction in Bose-Einstein condensates (BEC). The model hasan exact solution and allows us understand the mathematical technique used in this work and its limitations in a physical context. Next we investigate the role of non-linearity in higher orders in the revival times. This problem, technically very complicated could be solved with an algebraic technique developed by Carlos Heitor D'Avila Fonseca, from the Physics Department of UFMG. We showed that there is a dramatic qualitative change in the revival times. Next we study another model widely used in the literature to explore two BEC with mutual interaction. We investigate the revival times and the limitations of the techniques in all cases.