Dimension reduction for anisotropic Bose–Einstein condensates in the strong interaction regime. (12th February 2015)

• Record Type: Journal Article
• Authors: Bao, Weizhu; Treust, Loïc Le; Méhats, Florian
• Is Part Of: Nonlinearity. Volume 28:Number 3(2015:Mar.)
• Page Start: 755
• Page End: 772
• Publication Date: 2015-02-12
• Subjects: Gross–Pitaevskii equation -- dimension reduction -- semi-classical limit -- averaging -- asymptotic analysis -- highly oscillatory equations -- nonlinear Schrödinger equations; 35Q55 -- 35Q40; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/28/3/755
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We study the problem of dimension reduction for the three dimensional Gross–Pitaevskii equation (GPE) describing a Bose–Einstein condensate confined in a strongly anisotropic harmonic trap. Since the gas is assumed to be in a strong interaction regime, we have to analyse two combined singular limits: a semi-classical limit in the transport direction and the strong partial confinement limit in the transversal direction. We prove that both limits commute together and we provide convergence rates. The by-products of this work are approximated models in reduced dimension for the GPE, with a priori estimates of the approximation errors.