Vortices in a Bose-Einstein Condensate

Haljan, P. C.; Anderson, Brian P.; Matthews, M. R.; Hall, D. S.; Wieman, C. E.; Cornell, Eric A.

doi:10.1142/9789812813787_0077

Cited by 144 publications

(191 citation statements)

References 6 publications

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“…, m. The condition (1.8) is dictated by physical motivations. Indeed as we discussed before one of the main features of quantum fluids is the appearance of quantized vortices [29,61,75]. More precisely, quantum fluids are characterized by the fact that the flow is irrotational in the region {ρ > 0} and on the vacuum region quantized vortices may appear.…”

Section: Introductionmentioning

confidence: 89%

Remarks on the derivation of finite energy weak solutions to the QHD system

Antonelli

2021

Proc. Amer. Math. Soc.

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In this paper we consider the multi-dimensional Quantum Hydrodynamics (QHD) system, by adopting an intrinsically hydrodynamic approach. The present work continues the analysis initiated in [6] where the one dimensional case was studied. Here we extend the analysis to the multi-dimensional problem, in particular by considering two physically relevant classes of solutions. First of all we consider two-dimensional initial data endowed with point vortices; by assuming the continuity of the mass density and a quantization rule for the vorticity we are able to study the Cauchy problem and provide global finite energy weak solutions. The same result can be obtained also by considering spherically symmetric initial data in the multi-dimensional setting. For rough solutions with finite energy, we are able to provide suitable dispersive estimates, which also apply to a more general class of Euler-Korteweg equations.Moreover we are also able to show the sequential stability of weak solutions with positive density. Analogously to the one dimensional case this is achieved through the a priori bounds given by a new functional first introduced in [6].

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Section: Introductionmentioning

confidence: 89%

Remarks on the derivation of finite energy weak solutions to the QHD system

Antonelli

2021

Proc. Amer. Math. Soc.

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“…Physically this makes it impossible for a superfluid to rotate as a rigid body: In order to rotate, it must swirl [3]. The existence of quantized vortices with such particular pattern has been verified by experiments and numerics, see e.g., [40,7] and [1,16]. They can be observed in a condensate with either optical or magnetic traps.…”

Section: 1mentioning

confidence: 98%

“…The physical significance for NLS in a magnetic field is well-known in nonlinear optics and Bose-Einstein condensate (BEC), where the magnetic structure is involved in scattering, superfluid, quantized vortices as well as DNLS in plasma physics [40,29,46]. There have been produced BEC where Bosons, Femions or other quasi-particles are trapped with atomic lasers in order to observe the macroscopic coherent wave matter in ultra-cold temperature.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Schrödinger equations for Bose-Einstein condensates

Galati

Zheng

2013

AIP Conference Proceedings

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The Gross-Pitaevskii equation, or more generally the nonlinear Schrödinger equation, models the Bose-Einstein condensates in a macroscopic gaseous superfluid wave-matter state in ultra-cold temperature. We provide analytical study of the NLS with L 2 initial data in order to understand propagation of the defocusing and focusing waves for the BEC mechanism in the presence of electromagnetic fields. Numerical simulations are performed for the two-dimensional GPE with anisotropic quadratic potentials.

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“…j 2 R are the free parameters and represent the chemical potential, and V : R 2 7 ! R represents the trapping potential (see [1][2][3][4][5][6][7][8][9][10] and the references therein for further details). Clearly, these equations are of the form (1.1), and we shall discuss the implications of our results for these equations in Section 4.…”

Section: Introductionmentioning

confidence: 99%

Spots and stripes in nonlinear Schrödinger‐type equations with nearly one‐dimensional potentials

Hărăguş

Kapitula

2013

Math Methods in App Sciences

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We consider the existence of spots and stripes for a class of nonlinear Schrödinger‐type equations in the presence of nearly one‐dimensional localized potentials. Under suitable assumptions on the potential, we construct various types of waves that are localized in the direction of the potential and have single‐ or multihump, or periodic profile in the perpendicular direction. The analysis relies upon a spatial dynamics formulation of the existence problem, together with a center manifold reduction. This reduction procedure allows these waves to be realized as unipulse or multipulse homoclinic orbits, or periodic orbits in a reduced system of ordinary differential equations. Copyright © 2013 John Wiley & Sons, Ltd.

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Vortices in a Bose-Einstein Condensate

Cited by 144 publications

References 6 publications

Remarks on the derivation of finite energy weak solutions to the QHD system

Remarks on the derivation of finite energy weak solutions to the QHD system

Nonlinear Schrödinger equations for Bose-Einstein condensates

Spots and stripes in nonlinear Schrödinger‐type equations with nearly one‐dimensional potentials

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