LOCAL UNIQUENESS AND REFINED SPIKE PROFILES OF GROUND STATES FOR TWO-DIMENSIONAL ATTRACTIVE BOSE-EINSTEIN CONDENSATES

作者：Guo, Yujin^*; Lin, Changshou; Wei, Juncheng

来源：SIAM Journal on Mathematical Analysis, 2017, 49(5): 3671-3715.

DOI：10.1137/16M1100290

• Bose-Einstein condensation
• spike profiles
• local uniqueness
• Pohozaev identity

We consider ground states of two-dimensional Bose-Einstein condensates in a trap with attractive interactions, which can be described equivalently by positive minimizers of the L-2 -critical constraint Gross-Pitaevskii energy functional. It is known that ground states exist if and only if a < a* := ||omega||(2)(2), where a denotes the interaction strength and omega is the unique positive solution of Delta omega - omega + omega(3) - 0 in R-2. In this paper, we prove the local uniqueness and refined spike profiles of ground states as a NE arrow a*, provided that the trapping potential h(x) is homogeneous and H(y) = integral R-2 h(x + y)omega(2)(x)dx admits a unique and nondegenerate critical point.

• 出版日期2017
• 单位中国科学院武汉物理与数学研究所