JournalsaihpcVol. 33, No. 3pp. 809–828

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

  • Huan-Song Zhou

    Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, P.O. Box 71010, Wuhan 430071, PR China
  • Yujin Guo

    Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, P.O. Box 71010, Wuhan 430071, PR China
  • Xiaoyu Zeng

    Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, P.O. Box 71010, Wuhan 430071, PR China
Energy estimates and symmetry breaking in attractive Bose–Einstein condensates with ring-shaped potentials cover
Download PDF

Abstract

This paper is concerned with the properties of L2L^{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>0a > 0 approaches a critical value aa^{⁎}, 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 aaa↗a^{⁎}. However, when a>0a > 0 is suitably small we prove that the minimizers of the GP functional are unique, and this unique minimizer is radially symmetric.

Cite this article

Huan-Song Zhou, Yujin Guo, Xiaoyu Zeng, Energy estimates and symmetry breaking in attractive Bose–Einstein condensates with ring-shaped potentials. Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 3, pp. 809–828

DOI 10.1016/J.ANIHPC.2015.01.005