A Generalized-Laguerre--Fourier--Hermite Pseudospectral Method for Computing the Dynamics of Rotating Bose--Einstein Condensates

A time-splitting generalized-Laguerre-Fourier-Hermite pseudospectral method is proposed for computing the dynamics of rotating Bose-Einstein condensates (BECs) in two and three dimensions. The new numerical method is based on the following: (i) the use of a time-splitting technique for decoupling the nonlinearity; (ii) the adoption of polar coordinate in two dimensions, and resp. cylindrical coordinate in three dimensions, such that the angular rotation term becomes constant coefficient; and (iii) the construction of eigenfunctions for the linear operator by properly scale the generalized-Laguerre, Fourier and Hermite functions. The new method enjoys the following properties: (i) it is explicit, time reversible and time transverse invariant; (ii) it conserves the position density and is spectrally accurate in space and second-order or fourth-order accurate in time; and (iii) it solves the problem in the original whole space instead of in a truncated artificial computational domain. The method is also extended to solve the coupled Gross-Pitaevskii equations for the dynamics of rotating two-component and spin-1 BECs. Extensive numerical results for the dynamics of BECs are reported to demonstrate the accuracy and efficiency of the new method for rotating BECs.