Quasiperiodic dynamics in bose-einstein condensates in periodic lattices and superlattices
We 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 desc...
| Váldodahkkit: | , , , |
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| Materiálatiipa: | Journal article |
| Giella: | English |
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2007
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| _version_ | 1826306120405221376 |
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| author | Van Noort, M Porter, M Yi, Y Chow, S |
| author_facet | Van Noort, M Porter, M Yi, Y Chow, S |
| author_sort | Van Noort, M |
| collection | OXFORD |
| description | We 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 affects only scaling in phase space. Our approach is applicable to periodic superlattices with an arbitrary number of rationally dependent wave numbers. © 2006 Springer Science+Business Media, Inc. |
| first_indexed | 2024-03-07T06:43:08Z |
| format | Journal article |
| id | oxford-uuid:f9f8678b-68cf-48d4-a2d7-d24bc8303764 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:43:08Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:f9f8678b-68cf-48d4-a2d7-d24bc83037642022-03-27T13:02:02ZQuasiperiodic dynamics in bose-einstein condensates in periodic lattices and superlatticesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f9f8678b-68cf-48d4-a2d7-d24bc8303764EnglishSymplectic Elements at Oxford2007Van Noort, MPorter, MYi, YChow, SWe 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 affects only scaling in phase space. Our approach is applicable to periodic superlattices with an arbitrary number of rationally dependent wave numbers. © 2006 Springer Science+Business Media, Inc. |
| spellingShingle | Van Noort, M Porter, M Yi, Y Chow, S Quasiperiodic dynamics in bose-einstein condensates in periodic lattices and superlattices |
| title | Quasiperiodic dynamics in bose-einstein condensates in periodic lattices and superlattices |
| title_full | Quasiperiodic dynamics in bose-einstein condensates in periodic lattices and superlattices |
| title_fullStr | Quasiperiodic dynamics in bose-einstein condensates in periodic lattices and superlattices |
| title_full_unstemmed | Quasiperiodic dynamics in bose-einstein condensates in periodic lattices and superlattices |
| title_short | Quasiperiodic dynamics in bose-einstein condensates in periodic lattices and superlattices |
| title_sort | quasiperiodic dynamics in bose einstein condensates in periodic lattices and superlattices |
| work_keys_str_mv | AT vannoortm quasiperiodicdynamicsinboseeinsteincondensatesinperiodiclatticesandsuperlattices AT porterm quasiperiodicdynamicsinboseeinsteincondensatesinperiodiclatticesandsuperlattices AT yiy quasiperiodicdynamicsinboseeinsteincondensatesinperiodiclatticesandsuperlattices AT chows quasiperiodicdynamicsinboseeinsteincondensatesinperiodiclatticesandsuperlattices |