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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2002
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| Online-Zugang: | https://arxiv.org/abs/cond-mat/0210177 |
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| _version_ | 1866909853032644608 |
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| author | Muruganandam, Paulsamy Adhikari, Sadhan K |
| author_facet | Muruganandam, Paulsamy Adhikari, Sadhan K |
| contents | We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross-Pitaevskii (GP) equation and use it to study the resonance dynamics of a trapped Bose-Einstein condensate induced by a periodic variation in the atomic scattering length. When the frequency of oscillation of the scattering length is an even multiple of one of the trapping frequencies along the $x$, $y$, or $z$ direction, the corresponding size of the condensate executes resonant oscillation. Using the concept of the differentiation matrix, the partial-differential GP equation is reduced to a set of coupled ordinary differential equations which is solved by a fourth-order adaptive step-size control Runge-Kutta method. The pseudospectral method is contrasted with the finite-difference method for the same problem, where the time evolution is performed by the Crank-Nicholson algorithm. The latter method is illustrated to be more suitable for a three-dimensional standing-wave optical-lattice trapping potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_cond_mat_0210177 |
| institution | arXiv |
| publishDate | 2002 |
| record_format | arxiv |
| spellingShingle | Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods Muruganandam, Paulsamy Adhikari, Sadhan K Soft Condensed Matter Numerical Analysis Pattern Formation and Solitons We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross-Pitaevskii (GP) equation and use it to study the resonance dynamics of a trapped Bose-Einstein condensate induced by a periodic variation in the atomic scattering length. When the frequency of oscillation of the scattering length is an even multiple of one of the trapping frequencies along the $x$, $y$, or $z$ direction, the corresponding size of the condensate executes resonant oscillation. Using the concept of the differentiation matrix, the partial-differential GP equation is reduced to a set of coupled ordinary differential equations which is solved by a fourth-order adaptive step-size control Runge-Kutta method. The pseudospectral method is contrasted with the finite-difference method for the same problem, where the time evolution is performed by the Crank-Nicholson algorithm. The latter method is illustrated to be more suitable for a three-dimensional standing-wave optical-lattice trapping potential. |
| title | Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods |
| topic | Soft Condensed Matter Numerical Analysis Pattern Formation and Solitons |
| url | https://arxiv.org/abs/cond-mat/0210177 |