The nonexistence of vortices for rotating Bose-Einstein condensates in non-radially symmetric traps

Abstract

As a continuation of [34], we consider ground states of rotating Bose-Einstein condensates with attractive interactions in non-radially harmonic traps V(x)=x12+Λ2x22, where 0<Λ≠1 and x=(x1,x2)∈R2. For any fixed rotational velocity 0≤Ω<Ω⁎:=2min⁡{1,Λ}, it is known that ground states exist if and only if a<a⁎ for some critical constant 0<a⁎<∞, where a>0 denotes the product of the number of particles and the absolute value of the scattering length. We analyze the asymptotic expansions of ground states as a↗a⁎, which display the visible effect of Ω on ground states. As a consequence, we further prove that ground states do not have any vortex in the region R(a):={x∈R2:|x|≤C(a⁎−a)−112} as a↗a⁎ for some constant C>0, which is independent of 0<a<a⁎.