Quasiperiodic Dynamics in Bose-Einstein Condensates in Periodic Lattices and Superlattices

Simple item page
dc.creatorvan Noort, Martijn
dc.creatorPorter, Mason A.
dc.creatorYi, Yingfei
dc.creatorChow, Shui-Nee
dc.date2004-05-06
dc.date2006-09-18
dc.date.accessioned2026-07-07T06:36:45Z
dc.date.available2026-07-07T06:36:45Z
dc.descriptionWe employ KAM theory to rigorously investigate quasiperiodic dynamics in cigar-shaped Bose-Einstein condensates (BEC) in periodic lattices and superlattices. Toward this end, we apply a coherent structure ansatz to the Gross-Pitaevskii equation to obtain a parametrically forced Duffing equation describing the spatial dynamics of the condensate. For shallow-well, intermediate-well, and deep-well potentials, we find KAM tori and Aubry-Mather sets to prove that one obtains mostly quasiperiodic dynamics for condensate wave functions of sufficiently large amplitude, where the minimal amplitude depends on the experimentally adjustable BEC parameters. We show that this threshold scales with the square root of the inverse of the two-body scattering length, whereas the rotation number of tori above this threshold is proportional to the amplitude. As a consequence, one obtains the same dynamical picture for lattices of all depths, as an increase in depth essentially only affects scaling in phase space. Our approach is applicable to periodic superlattices with an arbitrary number of rationally dependent wave numbers.
dc.description29 pages, 6 figures (several with multiple parts; higher-quality versions of some of them available at http://www.its.caltech.edu/~mason/papers), to appear very soon in Journal of Nonlinear Science
dc.identifierhttps://arxiv.org/abs/math/0405112
dc.identifierhttp://arxiv.org/abs/math/0405112
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100188
dc.subjectDynamical Systems
dc.subjectSoft Condensed Matter
dc.subjectChaotic Dynamics
dc.subjectAtomic Physics
dc.subjectMSC: 37J40, 70H99, 37N20; PACS: 05.45.-a, 03.75.Lm, 05.30.Jp, 05.45.Ac, 03.75.Nt
dc.titleQuasiperiodic Dynamics in Bose-Einstein Condensates in Periodic Lattices and Superlattices
dc.typetext

Files

Collections

arXiv