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We construct a many-body Gaussian variational approach for the two-dimensional trapped Bose gas in the condensate phase. Interaction between particles is modelized by a generalized pseudopotential of zero range that allows recovering perturbative results in the ultradilute limit, while back action of noncondensate particles on the condensate part is taken into account for higher density. As an application, we derive the equation of state and solve stability problems encountered in similar mean-field formalisms for a single vortex configuration.
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Ludovic Pricoupenko (2004) studied this question.
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