English

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

Soft Condensed Matter 2025-10-20 v2 Numerical Analysis Numerical Analysis Pattern Formation and Solitons

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 xx, yy, or zz 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.

Keywords

Cite

@article{arxiv.cond-mat/0210177,
  title  = {Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods},
  author = {Paulsamy Muruganandam and Sadhan K Adhikari},
  journal= {arXiv preprint arXiv:cond-mat/0210177},
  year   = {2025}
}

Comments

14 Latex pages, 2 eps figures, accepted in Journal of Physics B