## Condensate density from Gross–Pitaevskii equation (24) (GP, dashed) and its fractional version (144 (FGP), both in the Thomas–Fermi approximation where the gradients are ignored

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**Figure 2.** Condensate density from Gross–Pitaevskii equation (24) (GP, dashed) and its fractional version (144 (FGP), both in the Thomas–Fermi approximation where the gradients are ignored. The FGP-curve shows a marked depletion of the condensate. On the right-hand side, a vortex is included. The zeros at *r* ≈ 1 will be smoothened by the gradient terms in (24) and (144), as shown on the left-hand plots without a vortex. The curves can be compared with those in [23–27].

**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.