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

2013-08-05T00:00:00Z (GMT) by Hagen Kleinert

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 [2327].

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.