Ground States and Dynamics of Multicomponent Bose-Einstein Condensates

We study numerically the time-independent vector Gross--Pitaevskii equations (VGPEs) for ground states and time-dependent VGPEs with (or without) an external driven field for dynamics describing a multicomponent Bose--Einstein condensate (BEC) at zero or a very low temperature. In preparation for the numerics, we scale the three-dimensional (3d) VGPEs, approximately reduce it to lower dimensions, present a continuous normalized gradient flow (CNGF) to compute ground states of multicomponent BEC, prove energy diminishing of the CNGF, which provides a mathematical justification, and discretize it by the backward Euler finite difference (BEFD), which is monotone in linear and nonlinear cases and preserves energy diminishing property in the linear case. Then we use a time-splitting sine-spectral (TSSP) method to discretize the time-dependent VGPEs with an external driven field for computing dynamics of multicomponent BEC. The merits of the TSSP method for VGPEs are that it is explicit, unconditionally stable,...

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