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

被引:121
作者
Guo, Yujin [1 ]
Zeng, Xiaoyu [1 ]
Zhou, Huan-Song [1 ]
机构
[1] Chinese Acad Sci, Wuhan Inst Phys & Math, POB 71010, Wuhan 430071, Peoples R China
来源
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2016年 / 33卷 / 03期
基金
中国国家自然科学基金;
关键词
Nonlinear elliptic equation; Constrained minimization; Gross-Pitaevskii functional; Bose-Einstein condensates; Attractive interactions; Ring-shaped potential; POSITIVE SOLUTIONS; DERIVATION; UNIQUENESS; EQUATIONS; VORTEX;
D O I
10.1016/j.anihpc.2015.01.005
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 NE arrow 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. (C) 2015 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码:809 / 828
页数:20
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