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arXiv:1301.5682 · Letters in Mathematical Physics

On the Mass Concentration for Bose–Einstein Condensates with Attractive Interactions

Yujin Guo, Robert Seiringer

Published Nov 20, 2013• 228 citations
arXivHTMLPDF
DOI
10.1007/s11005-013-0667-9

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This article is devoted to studying the model of two-dimensional attractive Bose-Einstein condensates in a trap V(x)V(x)V(x) rotating at the velocity $\Omega $. This model can be described by the complex-valued Gross-Pitaevskii energy functional. It is shown that there exists a critical rotational velocity 000 000 denotes the absolute product for the number of particles times the scattering length, and w>0w>0w>0 is the unique positive solution of Δw−w+w3=0\Delta w-w+w^3=0Δw−w+w3=0 in R2\mathbb{R}^2R2. If V(x)=∣x∣2V(x)=|x|^2V(x)=∣x∣2 and $ 0<\Omega <\Omega^*(=2)$ is fixed, we prove that, up to a constant phase, all minimizers must be real-valued, unique and free of vortices as a↗a∗a \nearrow a^*a↗a∗, by analyzing the refined limit behavior of minimizers and employing the non-degenerancy of www.