Particle-inspired scheme for the Gross-Pitaevski equation: An application to Bose--Einstein condensation

An explicit time-staggered scheme to solve the two-dimensional Gross-Pitaev ski equation in cylindrical geometry is presented. This scheme is an extens ion of the basic Visscher's algorithm to the case of a non-linear interacti on and non-Cartesian geometries. Drawing upon the Hamiltonian structure of the Schroedinger equation, this s cheme evolves the real and imaginary parts of the wavefunction in a way sim ilar to trajectory integration methods used in particle simulations. The scheme is demonstrated for the study of an expanding Bose-Einstein cond ensate. (C) 2000 Elsevier Science B.V. All rights reserved.