Ground states of attractive Bose gases near the critical rotating velocity.

We study ground states of attractive Bose gases, which are confined in a harmonic trap V (x) = x 1 2 + Λ x 2 2 ( Λ ≥ 1 ) rotating at the velocity Ω . For any 0 ≤ Ω < Ω ∗ : = 2 , where Ω ∗ is called a critical rotational velocity, it is well known that ground states exist if and only if a < a ∗ for some critical constant 0 < a ∗ < ∞ , where a > 0 denotes the product for the number of particles times the absolute value of the scattering length. In this paper, we consider the critical rotating case, where the rotational velocity Ω = Ω ∗ , to study the existence and non-existence of ground states with respect to a > 0 . As imposed in Remark 2.2 of Lewin et al. (Blow-up profile of rotating 2D focusing bose gases. macroscopic limits of quantum systems, Springer, Berlin, 2018), we also analyze the limiting behavior of ground states as a ↗ a ∗ for the case where Ω = Ω a : = Ω ∗ 1 - C 0 (a ∗ - a) m ↗ Ω ∗ , 0 ≤ m < 1 2 and 0 < C 0 < 1 . [ABSTRACT FROM AUTHOR]