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Hartree-Fock-Bogoliubov Model and Simulation of Attractive and Repulsive Bose-Einstein Condensates

We describe a model of dynamic Bose-Einstein condensates near a Feshbach resonance that is computationally feasible under assumptions of spherical or cylindrical symmetry. Simulations in spherical symmetry approximate the experimentally measured time to collapse of an unstably attractive condensate only when the molecular binding energy in the model is correct, demonstrating that the quantum fluctuations and atom-molecule pairing included in the model are the dominant mechanisms during collapse. Simulations of condensates with repulsive interactions find some quantitative disagreement, suggesting that pairing and quantum fluctuations are not the only significant factors for condensate loss or burst formation. Inclusion of three-body recombination was found to be inconsequential in all of our simulations, though we do not consider recent experiments [1] conducted at higher densities.