Minimal Mass-Energy Dynamics for Rotating BEC

I will review some recent progress concerning long time behaviors (existence, blowup and excited states) for the GrossPitaevskii equation with rotation. The GPE belongs in the type of magnetic nonlinear Schrödinger systems (mNLS) with a Lorentz gauge, which arises in modeling dilute, trapped boson gases with integer-spin in ultra-cold temperature.

Such system may exhibit interesting symmetries as well as stationary wave phenomenon, accompanied by spinor and quantized vortex, a remarkable signature for the superfluidity of Bose-Einstein condensation (BEC). I will discuss certain sharp criterion in terms of the mass and energy for the ground state in two and three dimensions.