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Thomas–Fermi profile of a fast rotating Bose–Einstein condensate

Dinh-Thi Nguyen and Nicolas Rougerie

Vol. 4 (2022), No. 3, 535–569
Abstract

We study the minimizers of a magnetic two-dimensional nonlinear Schrödinger energy functional in a quadratic trapping potential, describing a rotating Bose–Einstein condensate. We derive an effective Thomas–Fermi-like model in the rapidly rotating limit where the centrifugal force compensates the confinement and available states are restricted to the lowest Landau level. The coupling constant of the effective Thomas–Fermi functional is linked to the emergence of vortex lattices (the Abrikosov problem). We define it via a low-density expansion of the energy of the corresponding homogeneous gas in the thermodynamic limit.

Keywords
Abrikosov problem, Bose–Einstein condensates, Gross–Pitaevskii energy, lowest Landau level, Thomas–Fermi energy
Mathematical Subject Classification
Primary: 35Q40, 46N50, 81S05, 81V70
Milestones
Received: 18 January 2022
Accepted: 14 July 2022
Published: 4 December 2022
Authors
Dinh-Thi Nguyen
Unité de Mathématiques Pures et Appliquées
Ecole Normale Supérieure de Lyon & CNRS
Lyon
France
Nicolas Rougerie
Unité de Mathématiques Pures et Appliquées
Ecole Normale Supérieure de Lyon & CNRS
Lyon
France