Ground states of two-component attractive Bose–Einstein condensates I: Existence and uniqueness

Abstract

We study ground states of two-component Bose–Einstein condensates (BEC) with trapping potentials in R2, where the intraspecies interaction (−a1,−a2) and the interspecies interaction −β are both attractive, i.e, a1, a2 and β are all positive. The existence and non-existence of ground states are classified completely by investigating equivalently the associated L2-critical constraint variational problem. The uniqueness and symmetry-breaking of ground states are also analyzed under different types of trapping potentials as β↗β⁎=a⁎+(a⁎−a1)(a⁎−a2), where 0<ai<a⁎:=‖w‖22 (i=1,2) is fixed and w is the unique positive solution of Δw−w+w3=0 in R2. The semi-trivial limit behavior of ground states is tackled in the companion paper [12].