Recent Progress on Global Regularity for Rotating BEC

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As is known, the magnetic nonlinear Schrödinger equation (mNLS) is generated by the Hamiltonian HA,V, where A represents the magnetic potential and V the electric potential. The mNLS appears in modeling dilute, trapped boson gases with rotation in ultra-cold temperature, whose mechanism in the semiclassical regime obeys the Newton’s law in the transition from quantum to classical mechanics. Such systems 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). We study the fundamental solution for the propagator e −itHA,V. The earliest related result traces back to Feynman’s work on path integrals. Rigorous mathematical derivations were given by Fujiwara and Yajima. We further consider the threshold for the global regularity and blowup for mNLS. We will also briefly review current development in this perspective. Some numerical simulations are provided. Part of the work is collaboration with Luigi Galati.


International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory


Athens, GA