From Feshbach-Resonance Managed Bose-Einstein Condensates to Anisotropic Universes: Some Applications of the Ermakov-Pinney equation with Time-Dependent Nonlinearity

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dc.creatorHerring, G.
dc.creatorKevrekidis, P. G.
dc.creatorWilliams, F.
dc.creatorChristodoulakis, T.
dc.creatorFrantzeskakis, D. J.
dc.date2007-01-30
dc.date.accessioned2026-07-07T12:29:06Z
dc.date.available2026-07-07T12:29:06Z
dc.descriptionIn this work we revisit the topic of two-dimensional Bose-Einstein condensates under the influence of time-dependent magnetic confinement and time-dependent scattering length. A moment approach reduces the examination of moments of the wavefunction (in particular, of its width) to an Ermakov-Pinney (EP) ordinary differential equation (ODE). We use the well-known structure of the solutions of this nonlinear ODE to ``engineer'' trapping and interatomic interaction conditions that lead to condensates dispersing, breathing or even collapsing. The advantage of the approach is that it is fully tractable analytically, in excellent agreement with our numerical observations. As an aside, we also discuss how similar time-dependent EP equations may arise in the description of anisotropic scalar field cosmologies.
dc.description9 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0701756
dc.identifierhttp://arxiv.org/abs/cond-mat/0701756
dc.identifierPhys.Lett.A367:140-148,2007
dc.identifierdoi:10.1016/j.physleta.2007.01.087
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/215764
dc.subjectOther Condensed Matter
dc.titleFrom Feshbach-Resonance Managed Bose-Einstein Condensates to Anisotropic Universes: Some Applications of the Ermakov-Pinney equation with Time-Dependent Nonlinearity
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