Ground states of two-component Bose–Einstein condensates passing an obstacle
Liangshun Xu
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 Schrödinger 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.
Journal of Mathematical Physics•Jun 1, 2020•1 citation