Existence and mass concentration of 2D attractive Bose-Einstein condensates with periodic potentials
Existence and mass concentration of 2D attractive Bose-Einstein condensates with periodic potentials
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DOI：
10.1016/j.jde.2016.11.004
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发表时间：
2017-02
影响因子：
2.4
通讯作者：
Qingxuan Wang;Dun Zhao
中科院分区：
文献类型：
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作者：
Qingxuan Wang;Dun Zhao
本文考虑由Gross-Pitaevskii(GP)泛函描述的具有周期势的二维吸引玻色-爱因斯坦凝聚体。利用集中紧性引理，证明了当相互作用强度a满足⁎<；a<；a⁎时，对于某些常数a⁎≥0，a⁎>；0，该泛函存在极小元，而对于≥a⁎不存在极小元.当A逼近⁎时，我们再次使用集中紧性论证，得到依赖于周期势形状的最优能量估计。此外，我们还分析了质量浓度。
In this paper we consider a two-dimensional attractive Bose–Einstein condensate with periodic potential, described by Gross–Pitaevskii (GP) functional. By concentration-compactness lemma we show that minimizers of this functional exist when the interaction strength a satisfies a⁎< a< a⁎ for some constants a⁎≥ 0, a⁎> 0, and there is no minimizer for a≥ a⁎. When a approaches a⁎, using concentration-compactness arguments again we obtain an optimal energy estimate depending on the shape of periodic potential. Moreover, we analyze the mass concentration.