Stationary solutions for the nonlinear Schrodinger equation modeling three-dimensional spherical Bose-Einstein condensates in general potentials
Stationary solutions for the cubic nonlinear Schrödinger equation modeling Bose-Einstein condensates (BECs) confined in three spatial dimensions by general forms of a potential are studied through a perturbation method and also numerically. Note that we study both repulsive and attractive BECs unde...
| Main Authors: | , |
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| 格式: | Journal article |
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American Physical Society
2015
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| _version_ | 1826287586118729728 |
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| author | Mallory, K Van Gorder, R |
| author_facet | Mallory, K Van Gorder, R |
| author_sort | Mallory, K |
| collection | OXFORD |
| description | Stationary solutions for the cubic nonlinear Schrödinger equation modeling Bose-Einstein condensates (BECs) confined in three spatial dimensions by general forms of a potential are studied through a perturbation method and also numerically. Note that we study both repulsive and attractive BECs under similar frameworks in order to deduce the effects of the potentials in each case. After outlining the general framework, solutions for a collection of specific confining potentials of physical relevance to experiments on BECs are provided in order to demonstrate the approach. We make several observations regarding the influence of the particular potentials on the behavior of the BECs in these cases, comparing and contrasting the qualitative behavior of the attractive and repulsive BECs for potentials of various strengths and forms. Finally, we consider the nonperturbative where the potential or the amplitude of the solutions is large, obtaining various qualitative results. When the kinetic energy term is small (relative to the nonlinearity and the confining potential), we recover the expected Thomas-Fermi approximation for the stationary solutions. Naturally, this also occurs in the large mass limit. Through all of these results, we are able to understand the qualitative behavior of spherical three-dimensional BECs in weak, intermediate, or strong confining potentials. |
| first_indexed | 2024-03-07T02:00:52Z |
| format | Journal article |
| id | oxford-uuid:9d52252b-2f14-49bc-b359-0efce5eac86c |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:00:52Z |
| publishDate | 2015 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:9d52252b-2f14-49bc-b359-0efce5eac86c2022-03-27T00:42:06Z Stationary solutions for the nonlinear Schrodinger equation modeling three-dimensional spherical Bose-Einstein condensates in general potentials Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:9d52252b-2f14-49bc-b359-0efce5eac86cSymplectic Elements at OxfordAmerican Physical Society2015Mallory, KVan Gorder, R Stationary solutions for the cubic nonlinear Schrödinger equation modeling Bose-Einstein condensates (BECs) confined in three spatial dimensions by general forms of a potential are studied through a perturbation method and also numerically. Note that we study both repulsive and attractive BECs under similar frameworks in order to deduce the effects of the potentials in each case. After outlining the general framework, solutions for a collection of specific confining potentials of physical relevance to experiments on BECs are provided in order to demonstrate the approach. We make several observations regarding the influence of the particular potentials on the behavior of the BECs in these cases, comparing and contrasting the qualitative behavior of the attractive and repulsive BECs for potentials of various strengths and forms. Finally, we consider the nonperturbative where the potential or the amplitude of the solutions is large, obtaining various qualitative results. When the kinetic energy term is small (relative to the nonlinearity and the confining potential), we recover the expected Thomas-Fermi approximation for the stationary solutions. Naturally, this also occurs in the large mass limit. Through all of these results, we are able to understand the qualitative behavior of spherical three-dimensional BECs in weak, intermediate, or strong confining potentials. |
| spellingShingle | Mallory, K Van Gorder, R Stationary solutions for the nonlinear Schrodinger equation modeling three-dimensional spherical Bose-Einstein condensates in general potentials |
| title |
Stationary solutions for the nonlinear Schrodinger equation modeling three-dimensional spherical Bose-Einstein condensates in general potentials
|
| title_full |
Stationary solutions for the nonlinear Schrodinger equation modeling three-dimensional spherical Bose-Einstein condensates in general potentials
|
| title_fullStr |
Stationary solutions for the nonlinear Schrodinger equation modeling three-dimensional spherical Bose-Einstein condensates in general potentials
|
| title_full_unstemmed |
Stationary solutions for the nonlinear Schrodinger equation modeling three-dimensional spherical Bose-Einstein condensates in general potentials
|
| title_short |
Stationary solutions for the nonlinear Schrodinger equation modeling three-dimensional spherical Bose-Einstein condensates in general potentials
|
| title_sort | stationary solutions for the nonlinear schrodinger equation modeling three dimensional spherical bose einstein condensates in general potentials |
| work_keys_str_mv | AT malloryk stationarysolutionsforthenonlinearschrodingerequationmodelingthreedimensionalsphericalboseeinsteincondensatesingeneralpotentials AT vangorderr stationarysolutionsforthenonlinearschrodingerequationmodelingthreedimensionalsphericalboseeinsteincondensatesingeneralpotentials |