This paper is concerned with two-component Bose–Einstein condensates with both attractive intraspecies and interspecies interactions passing an obstacle in a plane, which can be described by the ground states of the nonlinear Schrodinger system defined in an exterior domain Ω=R2\ω, with ω⊂R2 being a bounded smooth convex domain. Under the assumption that the trapping potentials Vi(x) for i = 1, 2 attain their global minima only on the whole boundary ∂Ω, the existence, non-existence, and limiting behavior of ground states for the system are studied. When intraspecies interactions a1 and a2 satisfy 0 < a1, a2 < a* and interspecies interaction β satisfies 0 < β < β* by the delicate energy analysis, an optimal blow-up rate for ground states is also given as β ↗ β*, where β*=a*+(a*−a1)(a*−a2), a*≔‖Q‖22, and Q is the unique positive solution of ΔQ − Q + Q3 = 0 in R2.

中文翻译：

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两组分玻色-爱因斯坦凝聚体通过障碍物的基态

本文涉及双组分玻色-爱因斯坦凝聚，具有吸引力的种内和种间相互作用，可以通过平面中的障碍物，可以通过定义在外部域 Ω=R2\ω 中的非线性薛定谔系统的基态来描述，其中 ω⊂R2 是一个有界的光滑凸域。在假设 i = 1, 2 的俘获势 Vi(x) 仅在整个边界 ∂Ω 上达到其全局最小值的情况下，研究了系统基态的存在、不存在和限制行为。当种内相互作用 a1 和 a2 满足 0 < a1, a2 < a* 并且种间相互作用 β 满足 0 < β < β* 时，通过精细的能量分析，基态的最佳爆破率也为 β ↗ β*其中 β*=a*+(a*−a1)(a*−a2), a*≔‖Q‖22,