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dc.contributor.authorvan Noort, Martijn
dc.contributor.authorPorter, Mason
dc.contributor.authorYi, Yingfei
dc.contributor.authorChow, Shui-Nee
dc.date.accessioned2009-08-05T17:48:05Z
dc.date.available2009-08-05T17:48:05Z
dc.date.issued2005-07-23
dc.identifier.urihttp://hdl.handle.net/1853/29414
dc.descriptionMSC: 37J40, 70H99, 37N20 PACS: 05.45.-a, 03.75.Lm, 05.30.Jp, 05.45.Ac, 03.75.Nten
dc.description.abstractWe employ KAM theory to rigorously investigate the transition between quasiperiodic and chaotic 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 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 its amplitude essentially only affects scaling in phase space. Our approach is applicable to periodic superlattices with an arbitrary number of rationally dependent wave numbers.en
dc.language.isoen_USen
dc.publisherGeorgia Institute of Technologyen
dc.relation.ispartofseriesCDSNS2005-406en
dc.subjectHamiltonian dynamicsen
dc.subjectBose-Einstein condensatesen
dc.subjectKAM theoryen
dc.subjectAubry-Mather theoryen
dc.titleQuasiperiodic and Chaotic Dynamics in Bose-Einstein Condensates in Periodic Lattices and Superlatticesen
dc.typePre-printen
dc.contributor.corporatenameGeorgia Institute of Technology. School of Mathematics
dc.contributor.corporatenameImperial College, London. Dept. of Mathematics
dc.contributor.corporatenameCalifornia Institute of Technology. Dept. of Applied Physics and Materials Science
dc.contributor.corporatenameGeorgia Institute of Technology. Center for Dynamical Systems and Nonlinear Studies
dc.contributor.corporatenameCalifornia Institute of Technology. Center for the Physics of Information


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