2010/08/27 by Amandine Aftalion, Aftalion, Amandine, Robert L. Jerrard +3 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1008.4801
19 pages, no figures
arxiv created 2010/12/08 · arxiv updated 2010/12/09
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.