Existence and mass concentration of 2D attractive Bose-Einstein condensates with periodic potentials

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• 作者：Qingxuan Wang ; ^{wangqx12@lzu.edu.cn} ; Dun Zhao ^{zhaod@lzu.edu.cn}
• 关键词：Bose&ndash ; Einstein condensate ; Attractive interaction ; GP functional ; Periodic potential ; Energy estimate ; Mass concentration
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：262
• 期：3
• 页码：2684-2704
• 全文大小：339 K
• 卷排序：262

文摘

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⁎a⁎<a<a⁎ for some constants a⁎≥0a⁎≥0, a⁎>0a⁎>0, and there is no minimizer for a≥a⁎a≥a⁎. When a   approaches a⁎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.