Ground states of attractive Bose gases in rotating anharmonic traps

Abstract

This paper is concerned with ground states of attractive Bose gases confined in an anharmonic trap V(x)=ω(|x|2+k|x|4) rotating at the velocity Ω>0, where ω>0 denotes the trapping frequency, and k>0 represents the strength of the quartic term. It is known that for any Ω>0, ground states exist in such traps if and only if 0<a<a⁎, where a⁎:=‖Q‖22 and Q>0 is the unique positive solution of ΔQ−Q+Q3=0 in R2. By analyzing the refined energies and expansions of ground states, we prove that there exists a constant C>0, independent of 0<a<a⁎, such that ground states do not have any vortex in the region R(a):={x∈R2:|x|≤C(a⁎−a)−1−6β20} as a↗a⁎, for the case where ω=3Ω24, k=16, and Ω=C0(a⁎−a)−β varies for some β∈[0,16) and C0>0.