二维偶极玻色-爱因斯坦凝聚体的稳定性
On the stability of 2D dipolar Bose-Einstein condensates
摘要：
研究了具有偶极-偶极相互作用的玻色-爱因斯坦凝聚体的能量极小化的存在性。这个问题的关键在于，在波函数的质量守恒标度下，动能和（部分吸引的）相互作用能的行为是相同的。利用广义Gagliardo-Nirenberg不等式的最佳常数，得到了一个判别基态存在的精确判据.
英文摘要：
We study the existence of energy minimizers for a Bose-Einstein condensate with dipole-dipole interactions, tightly confined to a plane. The problem is critical in that the kinetic energy and the (partially attractive) interaction energy behave the same under mass-preserving scalings of the wave-function. We obtain a sharp criterion for the existence of ground states, involving the optimal constant of a certain generalized Gagliardo-Nirenberg inequality.
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