Ground states of attractive Bose gases near the critical rotating velocity

作者：Guo, Yujin^*; Li, Yan; Liu, Qiang; Lu, Lu

来源：Calculus of Variations and Partial Differential Equations, 2023, 62(7): 210.

DOI：10.1007/s00526-023-02547-x

• SCHRODINGER-EQUATIONS
• EINSTEIN CONDENSATION
• STANDING WAVES
• VORTEX
• STABILITY
• VORTICES

We study ground states of attractive Bose gases, which are confined in a harmonic trap V(x) = x(1)(2) + Lambda x(2)(2) (Lambda >= 1) rotating at the velocity Omega. For any 0 <= Omega < Omega* := 2, where Omega* 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 < alpha* < infinity, 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 Omega = Omega*, 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 NE arrow a* for the case where Omega = Omega(a)= Omega*root 1 - C-0(a* - a)(m) NE arrow Omega*, 0 m < 1/2 and 0 < C-0 < 1.