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
<p><strong>Figure 2.</strong> Condensate density from Gross–Pitaevskii equation (<a href="http://iopscience.iop.org/0953-4075/46/17/175401/article#jpb467377eqn24" target="_blank">24</a>) (GP, dashed) and its fractional version (<a href="http://iopscience.iop.org/0953-4075/46/17/175401/article#jpb467377eqn144" target="_blank">144</a> (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 <em>r</em> ≈ 1 will be smoothened by the gradient terms in (<a href="http://iopscience.iop.org/0953-4075/46/17/175401/article#jpb467377eqn24" target="_blank">24</a>) and (<a href="http://iopscience.iop.org/0953-4075/46/17/175401/article#jpb467377eqn144" target="_blank">144</a>), as shown on the left-hand plots without a vortex. The curves can be compared with those in [<a href="http://iopscience.iop.org/0953-4075/46/17/175401/article#jpb467377bib23" target="_blank">23</a>–<a href="http://iopscience.iop.org/0953-4075/46/17/175401/article#jpb467377bib27" target="_blank">27</a>].</p> <p><strong>Abstract</strong></p> <p>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.</p>