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Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods

Paulsamy Muruganandam·Sadhan K Adhikari
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Abstract

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.

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Paulsamy Muruganandam, Sadhan K Adhikari. 2003-05-02. Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods. https://doi.org/10.1088/0953-4075%2F36%2F12%2F310

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