title: Approximate mean-field equations of motion for quasi-two-dimensional Bose-Einstein-condensate systems.
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.
authors.affiliation: Department of Physics, Georgia Southern University, Statesboro, Georgia 30460-8031, USA.
authors.forename: Mark
authors.initials: M
authors.lastname: Edwards
authors.forename: Michael
authors.initials: M
authors.lastname: Krygier
authors.forename: Hadayat
authors.initials: H
authors.lastname: Seddiqi
authors.forename: Brandon
authors.initials: B
authors.lastname: Benton
authors.forename: Charles W
authors.initials: CW
authors.lastname: Clark
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008962:Models, Theoretical; D011789:Quantum Theory; D013816:Thermodynamics