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

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posted on 05.08.2013, 00:00 by Hagen Kleinert

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


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.