Mass concentration behavior of Bose–Einstein condensates with attractive interactions in bounded domains. Issue 14 (25th October 2020) - Luo, Yong; Zhu, Xincai
ABSTRACT: We study the Bose–Einstein condensates with attractive interaction in a bounded domain Ω ⊂ R 2, described by Gross–Pitaevskii energy functional. We prove that there exists a constant a ∗ > 0, such that minimizers exist if and only if 0 < a < a ∗ . As a ↗ a ∗, the limit behavior of minimizers is also analyzed, where the mass must concentrate at the global minimum points of the trapping potential V ( x ) . In particular, if V ( x ) has the flattest global minimum points both at the interior and the boundary of Ω, we prove that the mass must concentrate at an inner minimum point of Ω, rather than the neighborhood of the boundary minimum points.