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

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 $a<a^{\ast }=\Vert Q{\Vert }_2^2$, where $Q$ is the unique positive radial solution of $\Delta u-u+u^3=0$ in ${\mathbb{R}}^2$. We present a detailed analysis of the behavior of minimizers as $a$ approaches $a^{\ast }$, where all the mass concentrates at a global minimum of the trapping potential.

LaTeX, 14 pages; revised version, to appear in Lett. Math. Phys

References in corpus (3)

• Many-Body Physics with Ultracold Gases
• Energy estimates and symmetry breaking in attractive Bose-Einstein condensates with ring-shaped potentials
• Optimal trap shape for a Bose gas with attractive interactions

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