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arXiv · 1612.03295

Local Uniqueness and Refined Spike Profiles of Ground States for Two-Dimensional Attractive Bose-Einstein Condensates

Yujin Guo·Changshou Lin·Juncheng Wei
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Abstract

We consider ground states of two-dimensional Bose-Einstein condensates in a trap with attractive interactions, which can be described equivalently by positive minimizers of the $L^2-$critical constraint Gross-Pitaevskii energy functional. It is known that ground states exist if and only if $a< a^*:= \|w\|_2^2$, where $a$ denotes the interaction strength and $w$ is the unique positive solution of $\Delta w-w+w^3=0$ in $R^2$. In this paper, we prove the local uniqueness and refined spike profiles of ground states as $a\nearrow a^*$, provided that the trapping potential $h(x)$ is homogeneous and $H(y)=\int_{R^2} h(x+y)w^2(x)dx$ admits a unique and non-degenerate critical point.

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Yujin Guo, Changshou Lin, Juncheng Wei. 2016-12-10. Local Uniqueness and Refined Spike Profiles of Ground States for Two-Dimensional Attractive Bose-Einstein Condensates. https://arxiv.org/abs/1612.03295

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