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Vortex lattices in rotating Bose-Einstein condensates. (English) Zbl 1174.35104
Summary: The structure of the vortex lattice for a fast rotating condensate in a harmonic trap has been studied experimentally and numerically: it is an almost regular hexagonal lattice, with a distortion on the edges. In this paper, we provide rigorous proofs of results announced in [A. Aftalion, X. Blanc and J. Dalibard, Phys. Rev. A 71, 023611 (2005)]. We analyze the vortex pattern in the framework of the Gross-Pitaevskii energy using wave functions in the lowest Landau level. We compute the energy of a regular triangular lattice and of a class of distorted lattices and find the optimal distortion which provides a decay of the wave function similar to an inverted parabola.
MSC:
35Q55NLS-like (nonlinear Schrödinger) equations
35Q40PDEs in connection with quantum mechanics
35A15Variational methods (PDE)
81V45Applications of quantum theory to atomic physics
82D50Superfluids (statistical mechanics)
82B10Quantum equilibrium statistical mechanics (general)
81V80Applications of quantum theory to quantum optics