Effective action and field equation for BEC from weak to strong couplings

While free and weakly interacting nonrelativistic particles are described by a Gross-Pitaevskii equation, which is a nonlinear self-interacting Schrödinger equation, the phenomena in the strong-coupling limit are governed by an effective action that is extremized by a double-fractional generalization of this equation. Its particle orbits perform Lévy walks rather than Gaussian random walks