Effective Action and Field Equation for BEC from Weak to Strong Couplings

Abstract

While free and weakly interacting nonrelativistic particles are described by a Gross-Pitaevskii equation, which is a nonlinear self-interacting Schr\"odinger 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 L\`evy walks rather than Gaussian random walks.