Weakly Nonlinear Analysis of Vortex Formation in a Dissipative Variant of the Gross-Pitaevskii Equation
TLDR
In this article, the authors studied a symmetry breaking process that leads to the formation of vortices in a dissipative version of the Gross-Pitaevskii equation with a parabolic trap under rotation.Abstract:
For a dissipative variant of the two-dimensional Gross--Pitaevskii equation with a parabolic trap under rotation, we study a symmetry breaking process that leads to the formation of vortices. The first symmetry breaking leads to the formation of many small vortices distributed uniformly near the Thomas--Fermi radius. The instability occurs as a result of a linear instability of a vortex-free steady state as the rotation is increased above a critical threshold. We focus on the second subsequent symmetry breaking, which occurs in the weakly nonlinear regime. At slightly above threshold, we derive a one-dimensional amplitude equation that describes the slow evolution of the envelope of the initial instability. We show that the mechanism responsible for initiating vortex formation is a modulational instability of the amplitude equation. We also illustrate the role of dissipation in the symmetry breaking process. All analyses are confirmed by detailed numerical computations.read more
Citations
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Journal ArticleDOI
Multi-vortex crystal lattices in Bose-Einstein condensates with a rotating trap.
TL;DR: In this article, the authors derived a reduced system of ODEs that describes stable configurations of multiple co-rotating vortices (vortex crystals) in the context of Bose-Einstein condensates with a rotating trap.
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Multi-vortex crystal lattices in Bose-Einstein Condensates with a rotating trap
TL;DR: A novel reduced system of ordinary differential equations (ODEs) that describes stable configurations of multiple co-rotating vortices (vortex crystals) is derived, found to be quite accurate quantitatively especially in the case of multiple vortice.
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Influence of Dissipation on the Vortex Motion in Rotating Bose–Einstein Condensates
TL;DR: In this paper, a strongly anisotropic magnetic trap whose trapping potential is much higher in the direction z than in the transverse direction is considered, where the condensate takes the form of a plane disk.
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