BoseEinstein condensation dynamics in three dimensions by the pseudospectral and finitedifference methods
Abstract
We suggest a pseudospectral method for solving the threedimensional timedependent GrossPitaevskii (GP) equation, and use it to study the resonance dynamics of a trapped BoseEinstein 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 partialdifferential GP equation is reduced to a set of coupled ordinary differential equations, which is solved by a fourthorder adaptive stepsize control RungeKutta method. The pseudospectral method is contrasted with the finitedifference method for the same problem, where the time evolution is performed by the CrankNicholson algorithm. The latter method is illustrated to be more suitable for a threedimensional standingwave opticallattice trapping potential.
 Publication:

Journal of Physics B Atomic Molecular Physics
 Pub Date:
 June 2003
 DOI:
 10.1088/09534075/36/12/310
 arXiv:
 arXiv:condmat/0210177
 Bibcode:
 2003JPhB...36.2501M
 Keywords:

 Condensed Matter  Soft Condensed Matter;
 Mathematics  Numerical Analysis;
 Nonlinear Sciences  Pattern Formation and Solitons
 EPrint:
 14 Latex pages, 2 eps figures, accepted in Journal of Physics B