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 $0 0$ is the unique positive solution of $ΔQ-Q+Q^{3}=0$ in $\mathbb{R}^2$. By analyzing the refined energies and expansions of ground states, we prove that there exists a constant $C>0$, independent of $0 0$.