Non existence of vortices in the small density region of a condensate

Details Non existence of vortices in the small density region of a condensate Non existence of vortices in the small density region of a condensate

2010-08-27

arxiv.org/abs/1008.4801v2

Physics

Mathematical Physics

19 pages, no figures

Scientific paper

In this paper, we answer a question raised by Len Pitaevskii and prove that the ground state of the Gross-Pitaevskii energy describing a Bose Einstein condensate at low rotation does not have vortices in the low density region. Therefore, the first ground state with vortices has its vortices in the bulk. This is obtained by proving that for small rotational velocities, the ground state is multiple of the ground state with zero rotation. We rely on sharp bounds of the decay of the wave function combined with weighted jacobian estimates.

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