Document Type
Article
Publication Date
11-2012
Publication Title
Physical Review E
DOI
10.1103/PhysRevE.86.056710
ISSN
2470-0045
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.
Recommended Citation
Edwards, Mark, Michael Krygier, Hadayat Seddiqi, Brandon Benton, Charles W. Clark.
2012.
"Approximate Mean-field Equations of Motion for Quasi-two-dimensional Bose-Einstein Condensates."
Physical Review E, 86 (056710): American Physical Society.
doi: 10.1103/PhysRevE.86.056710 source: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.86.056710
https://digitalcommons.georgiasouthern.edu/physics-facpubs/20
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.