A Time-Splitting and Sine Spectral Method for Dynamics of Dipolar Bose-Einstein Condensate

الملخص EN

A two-component Bose-Einstein condensate (BEC) described by two coupled a three-dimension Gross-Pitaevskii (GP) equations is considered, where one equation has dipole-dipole interaction while the other one has only the usual s-wave contact interaction, in a cigar trap.

The time-splitting and sine spectral method in space is proposed to discretize the time-dependent equations for computing the dynamics of dipolar BEC.

The singularity in the dipole-dipole interaction brings significant difficulties both in mathematical analysis and in numerical simulations.

Numerical results are given to show the efficiency of this method.