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arXiv · 1301.5682

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

Yujin Guo·Robert Seiringer
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Abstract

We consider two-dimensional Bose-Einstein condensates with attractive interaction, described by the Gross-Pitaevskii functional. Minimizers of this functional exist only if the interaction strength $a$ satisfies $a < a^*= \|Q\|_2^2$, where $Q$ is the unique positive radial solution of $Δu-u+u^3=0$ in $\R^2$. We present a detailed analysis of the behavior of minimizers as $a$ approaches $a^*$, where all the mass concentrates at a global minimum of the trapping potential.

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Yujin Guo, Robert Seiringer. 2013-10-24. On the Mass Concentration for Bose-Einstein Condensates with Attractive Interactions. https://doi.org/10.1007/s11005-013-0667-9

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