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Communications in Mathematical Physics

, Volume 303, Issue 2, pp 451–508 | Cite as

The Transition to a Giant Vortex Phase in a Fast Rotating Bose-Einstein Condensate

  • M. Correggi
  • N. Rougerie
  • J. YngvasonEmail author
Article

Abstract

We study the Gross-Pitaevskii (GP) energy functional for a fast rotating Bose-Einstein condensate on the unit disc in two dimensions. Writing the coupling parameter as 1/ε 2 we consider the asymptotic regime ε → 0 with the angular velocity Ω proportional to (ε 2|log ε|)−1. We prove that if Ω = Ω0(ε 2|log ε|)−1 and Ω0 > 2(3π)−1 then a minimizer of the GP energy functional has no zeros in an annulus at the boundary of the disc that contains the bulk of the mass. The vorticity resides in a complementary ‘hole’ around the center where the density is vanishingly small. Moreover, we prove a lower bound to the ground state energy that matches, up to small errors, the upper bound obtained from an optimal giant vortex trial function, and also that the winding number of a GP minimizer around the disc is in accord with the phase of this trial function.

Keywords

Vortex Vorticity Ground State Energy Trial Function Giant Vortex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.CIRM, Fondazione Bruno KesslerTrentoItaly
  2. 2.Laboratoire Jacques-Louis LionsUniversité Pierre et Marie CurieParisFrance
  3. 3.Erwin Schrödinger Institute for Mathematical PhysicsViennaAustria
  4. 4.Fakultät für PhysikUniversität WienViennaAustria

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