Abstract
The Bogoliubov approximation and the Gross-Pitaevskii equation characterize the effect of repulsive interactions on a dilute ideal Bose-Einstein gas in a spherical harmonic trap. For large N, the interactions expand the condensate relative to an ideal Bose gas; both the speed of sound and critical angular velocity Ωc1 for creation of a quantized vortex depend crucially on the interparticle repulsion through the coherence length ξ.
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