Note on rotating BEC under a confining potential

Abstract

Recently there have been analytical studies concerning the threshold on the instability for a rotating BEC under a trapping potential. In this note, we obtain a critical lower bound μ∗that ensures the existence of ground state solutions for the L2-critical RNLS in 2dand 3d, where an anisotropic harmonic potential is present. In addition, we perform numerical estimation for the corresponding stationary equation for the ground state and the vortex state solutions. Our findings indicate agreement on the sharp bound from both analytical and numerical demonstration. Among others we prove a blowup alternative result for RNLS with an inhomogeneous nonlinearity.

Keywords

• RNLS
• Threshold
• Ground state
• Harmonic potential
• Angular momentum