A time-splitting spectral method for computing dynamics of spinor F=1 Bose-Einstein condensates

Abstract

We propose a time-splitting spectral method for the generalized Gross-Pitaevskii equations, which describe the dynamics of spinor F=1 Bose-Einstein condensates at a very low temperature. The new numerical method is explicit, unconditionally stable, and of spectral accuracy in space. Moreover, it conserves the position densities at the discretized level. We apply the method for studying both the dynamic generation of vortices and vortex lattice dynamics for the spinor F=1 Bose-Einstein condensates held in an Ioffe-Pritchard magnetic field.