Dynamics of Rotating Two-component Bose-Einstein Condensates and Its Efficient Computation
In this paper, we investigate the dynamics of rotating two-component Bose-Einstein condensates (BEC) based on the coupled Gross-Pitaevskiiequations (CGPEs) with an angular momentum rotation term and an external driving field, and propose an efficient and accurate method fornumerical simulations. We prove the conservation of the angular momentum expectation, derive the dynamic laws for the density of eachcomponent and condensate widths, and analyze the dynamics of a stationary state with its center shifted from the trap center. By formulatingthe CGPEs in either 2D (two-dimensional) polar coordinate or 3D cylindrical coordinate system, the angular momentum rotation term becomesa term with constant coefficients. This allows us to develop an efficient time-splitting method which is time reversible, time transverse invariant,unconditionally stable, efficient and accurate for the problem. Moreover, it conserves the total position density in the discretized level. Thenumerical method is applied to verify our analytical results and study the dynamics of quantized vortex lattices in rotating two-component BECwith/without an external driving field.
Y. Zhang et al., "Dynamics of Rotating Two-component Bose-Einstein Condensates and Its Efficient Computation," Physica D: Nonlinear Phenomena, Elsevier, Jan 2007.
The definitive version is available at https://doi.org/10.1016/j.physd.2007.06.026
Mathematics and Statistics
Keywords and Phrases
rotating two-component Bose-Einstein condensation; coupled Gross-Pitavskii equations; Angular momentum rotation; condensate width; angular momentum expectation; quantized vortex lattice
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