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Abstract:
In this talk, we present efficient and stable numerical methods to compute
ground states and dynamics of Bose-Einstein condensates (BEC) in a
rotational frame. As preparatory steps, we take the 3D Gross-Pitaevskii
equation (GPE) with an angular momentum rotation, scale it to obtain a
four-parameter model and show how to reduce it to 2D GPE in certain
limiting regimes. Then we study numerically and asymptotically the ground
states, excited states and quantized vortex states as well as their energy
and chemical potential diagram in rotating BEC. Some very interesting
numerical results are observed. Finally, we study numerically stability
and interaction of quantized vortices in rotating BEC. Some interesting
interaction patterns will be reported.
This talk is based on joint work with Qiang Du, Peter Markowich, Hanquan
Wang and Yanzhi Zhang. |