Analysis and Efficient Computation for the Dynamics of Two-Component Bose-Einstein Condensates

In this paper, we review some recent results on the analysis and efficient computation for the dynamics of rotating two-component Bose-Einstein condensates (BECs). We begin with the three-dimensional (3D) coupled GrossPitaevskii equations (GPEs) with an angular momentum rotation term and an external driving field, show how to scale it into dimensionless form, reduce it to a 2D and 1D GPE in the limiting regime of strong anisotropic confinement and present its semiclassical scaling and geometric optics. Dynamic laws on the angular momentum expectation, density of each component, condensate widths and analytical solutions of stationary states with its center shifted from the trapping center are presented. In addition, efficient and accurate numerical methods for computing the dynamics of rotating two-component BEC are presented and some numerical results are reported to demonstrate the efficiency and accuracy of the numerical methods.