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- W2083561837 abstract "We study the numerical solution of the time-dependent Gross-Pitaevskii equation (GPE) describing a Bose-Einstein condensate (BEC) at zero or very low temperature. In preparation for the numerics we scale the 3d Gross-Pitaevskii equation and obtain a four-parameter model. Identifying `extreme parameter regimes', the model is accessible to analytical perturbation theory, which justifies formal procedures well known in the physical literature: reduction to 2d and 1d GPEs, approximation of ground state solutions of the GPE and geometrical optics approximations. Then we use a time-splitting spectral method to discretize the time-dependent GPE. Again, perturbation theory is used to understand the discretization scheme and to choose the spatial/temporal grid in dependence of the perturbation parameter. Extensive numerical examples in 1d, 2d and 3d for weak/strong interactions, defocusing/focusing nonlinearity, and zero/nonzero initial phase data are presented to demonstrate the power of the numerical method and to discuss the physics of Bose-Einstein condensation." @default.
- W2083561837 created "2016-06-24" @default.
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- W2083561837 date "2003-05-01" @default.
- W2083561837 modified "2023-10-17" @default.
- W2083561837 title "Numerical solution of the Gross–Pitaevskii equation for Bose–Einstein condensation" @default.
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- W2083561837 doi "https://doi.org/10.1016/s0021-9991(03)00102-5" @default.
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