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Numerical solution of the gross-pitaevskii equation using an explicit finite-difference scheme: An application to trapped bose-einstein condensates

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Istituto Applicazioni Calcolo "M. Picone," Via del Policlinico 137, I-00161 Roma, Italy.


We present the application of a fast, explicit time-marching scheme for the solution of the Gross-Pitaevskii equation in cylindrical geometry. The scheme is validated on simple analytical tests and demonstrated for two situations of physical interest in experiments on the Bose-Einstein condensation (BEC) of trapped alkali-metal vapors. It is tested by reproducing known results on the free expansion of a BEC after removing a cylindrical trap, and it is then used to address the formation of matter-wave pulses that result from gravity-induced transport of a condensate in an optical potential.

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