2010/09/10 by Nicolas Rougerie, Rougerie, Nicolas
Mathematics · Physics and Astronomy · #35Q55 #47.32.-y #47.37.+q #47J30 #76M23. PACS: 03.75.Hh #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #math-ph #math.MP #msc:03.75.Hh #msc:35Q55 #msc:47.32.-y #msc:47J30 #msc:76M23.
paper · pdf · doi:10.48550/arxiv.1009.1968
21 pages, 4 figures. To appear in Applied Mathematic Research Express. This is an expanded and upgraded version of [X.Blanc, N.Rougerie, Lowest-Landau-Level vortex structure of a Bose-Einstein condensate rotating in a harmonic plus quartic trap, arXiv:0801.3571, Phys. Rev. A 77 (2008)]
arxiv created 2010/11/17 · arxiv updated 2010/11/18
A rotating superfluid such as a Bose-Einstein condensate is usually described by the Gross-Pitaevskii (GP) model. An important issue is to determine from this model the properties of the quantized vortices that a superfluid nucleates when set into rotation. In this paper we address the minimization of a two dimensional GP energy functional describing a rotating annular Bose-Einstein condensate. In a certain limit it is physically relevant to restrict the minimimization to the Lowest-Landau-Level, that is the first eigenspace of the Ginzburg-Landau operator. Taking the particular structure of this space into account we obtain theoretical results concerning the vortices of the condensate. We also compute the vortices' locations by a numerical minimization procedure. We find that they lie on a distorted lattice and that multiply quantized vortices appear in the central hole of low matter density.