Redução dimensional para condensados de Bose-Einstein em forma de “tubo” e “anilha plana”

Abstract

The study of nonlinear dynamics represents a challenge of contemporary physics. In particular, the investigation of Bose Einstein condensates proved to be a hard task due to the large number of interacting particles. Therefore, given the difficulty of modeling these systems, approximations were introduced, which promoted the description of the Bose-Einstein condensation state in interacting atomic gases as a three-dimensional nonlinear Schrödinger equation, known as the Gross-Pitaevskii equation. In this work we review the dimensional reduction method, which use a variational treatment with the goal of derive effective one-dimensional (1D) and two-dimensional (2D) equations in cigar-shaped and pancake-shaped Bose-Einstein condensates, where we show that these equations describe almost exactly the dynamics of their respective models. Thus, we studied the ground-state solutions in tube-shaped and flat washer-shaped Bose-Einstein condensates by means of effectives non-polynomials equations, derived from the dimensional reduction method. The results produced by this equations were in very good agreement with those obtained from the corresponding full 3D Gross-Pitaevskii equation.