Energy estimates and symmetry breaking in attractive Bose-Einstein condensates with ring-shaped potentials

By Yujin Guo, Xiaoyu Zeng, Huan-Song Zhou. 2014

173 citations recorded by the source corpus.

This paper is concerned with the properties of $L^2$-normalized minimizers of the Gross-Pitaevskii (GP) functional for a two-dimensional Bose-Einstein condensate with attractive interaction and ring-shaped potential. By establishing some delicate estimates on the least energy of the GP functional, we prove that symmetry breaking occurs for the minimizers of the GP functional as the interaction strength $a>0$ approaches a critical value $a^*$, each minimizer of the GP functional concentrates to a point on the circular bottom of the potential well and then is non-radially symmetric as $a\nearrow a^*$. However, when $a>0$ is suitably small we prove that the minimizers of the GP functional are unique, and this unique minimizer is radially symmetric.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/7b774a67c044e4ffe337d5c99e08f542f955c14b

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In Atomic and Molecular Physics, and Optics

1. Yujin Guo
2. Robert Seiringer
3. Hongyu Ye
4. Mathieu Lewin
5. Phan Thanh Nam
6. Philip D. Grech

Citations in the corpus

• On the Mass Concentration for Bose–Einstein Condensates with Attractive Interactions (2013, background): “We note that new ingredients in the proof are needed to treat the case of radially symmetric, ring-shaped potentials (with a continuum of minima) and the corresponding analysis will be presented elsewhere [17].”