Manipulations of Coherent Matter-Waves

Kevrekidis, P. G.; Frantzeskakis, D. J.; Carretero-González, R.

doi:10.1007/978-3-540-73591-5_17

Cited by 2 publications

(3 citation statements)

References 94 publications

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“…On the other hand, a natural generalization of the present considerations is that of exploring the dynamics of vortex rings in three-dimensional BECs; see e.g. [3,44] for relevant reviews. In this context, it is also possible to write ordinary differential equations characterizing the interaction of the rings and their intrinsic translational dynamics as e.g.…”

Section: Conclusion and Future Challengesmentioning

confidence: 98%

“…The realm of Bose-Einstein condensates (BECs) has offered in the past two decades a pristine setting for the exploration of numerous nonlinear wave structures and their interactions [1,2,3]. One of the most prominent examples of such states that has received considerable attention consists of matter wave vortices, which have by now been reviewed in numerous works [4,5,6,7,8].…”

Section: Introductionmentioning

confidence: 99%

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Few-particle vortex cluster equilibria in Bose–Einstein condensates: existence and stability

Barry¹,

Kevrekidis²

2013

J. Phys. A: Math. Theor.

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Abstract. Motivated by recent experimental and theoretical studies of fewparticle vortex clusters in Bose-Einstein condensates, we consider the ordinary differential equations of motion and systematically examine settings for up to N = 6 vortices. We analyze the existence of corresponding stationary state configurations and also consider their spectral stability properties. We compare our particle model results with the predictions of the full partial differential equation system. Whenever possible, we propose generalizations of these results in the context of clusters of N vortices. Some of these, we can theoretically establish, especially so for the N-vortex polygons, while others we state as conjectures, e.g. for the N-vortex line equilibrium.

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Section: Conclusion and Future Challengesmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Few-particle vortex cluster equilibria in Bose–Einstein condensates: existence and stability

Barry¹,

Kevrekidis²

2013

J. Phys. A: Math. Theor.

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“…That involves the dynamics of matter waves in ultra-cold atoms and more specifically in the theme of Bose-Einstein condensates (BECs) [5,6,7]. There, the ability to stir the system (imparting angular momentum), or to quench it (spontaneously locking in vortex patterns), or to drag obstacles through it (producing vorticity through the breakup of superfluidity) enables the spontaneous production of one or more vortices, as has now been summarized in numerous works [8,9,10,11,12].…”

Section: Introductionmentioning

confidence: 99%

Generating functions, polynomials and vortices with alternating signs in Bose–Einstein condensates

Barry

Hajir

2015

J. Phys. A: Math. Theor.

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Abstract. In this work, we construct suitable generating functions for vortices of alternating signs in the realm of Bose-Einstein condensates. In addition to the vortex-vortex interaction included in earlier fluid dynamics constructions of such functions, the vortices here precess around the center of the trap. This results in the generating functions of the vortices of positive charge and of negative charge satisfying a modified, so-called, Tkachenko differential equation. From that equation, we reconstruct collinear few-vortex equilibria obtained in earlier work, as well as extend them to larger numbers of vortices. Moreover, particular moment conditions can be derived e.g. about the sum of the squared locations of the vortices for arbitrary vortex numbers. Furthermore, the relevant differential equation can be generalized appropriately in the two-dimensional complex plane and allows the construction e.g. of polygonal vortex ring and multi-ring configurations, as well as ones with rings surrounding a vortex at the center that are again connected to earlier bibliography.

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Manipulations of Coherent Matter-Waves

Cited by 2 publications

References 94 publications

Few-particle vortex cluster equilibria in Bose–Einstein condensates: existence and stability

Few-particle vortex cluster equilibria in Bose–Einstein condensates: existence and stability

Generating functions, polynomials and vortices with alternating signs in Bose–Einstein condensates

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