Document Type

Article

Publication Date

11-2012

Publication Title

Physical Review E

DOI

10.1103/PhysRevE.86.056710

Abstract

We present a method for approximating the solution of the three-dimensional, time-dependent Gross-Pitaevskii equation (GPE) for Bose-Einstein-condensate systems where the confinement in one dimension is much tighter than in the other two. This method employs a hybrid Lagrangian variational technique whose trial wave function is the product of a completely unspecified function of the coordinates in the plane of weak confinement and a Gaussian in the strongly confined direction having a time-dependent width and quadratic phase. The hybrid Lagrangian variational method produces equations of motion that consist of (1) a two-dimensional (2D) effective GPE whose nonlinear coefficient contains the width of the Gaussian and (2) an equation of motion for the width that depends on the integral of the fourth power of the solution of the 2D effective GPE. We apply this method to the dynamics of Bose-Einstein condensates confined in ring-shaped potentials and compare the approximate solution to the numerical solution of the full 3D GPE.

Comments

Authors have the right to use all or part of the Article, including the APS-prepared version without revision or modification, on the author(s)’ web home page or employer’s website. (source:http://journals.aps.org/authors/transfer-of-copyright-agreement) Article obtained from Physical Review E.

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