Solution of the variational equation (130) for ar{f}_1=1

Figure 1. Solution of the variational equation (130) for \bar{f}_1=1. The dotted curves show the pure large-y behaviour.

Abstract

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.