We investigate the physics underlying the presence of a quasicondensate in a nearly one dimensional, weakly interacting trapped atomic Bose gas. We show that a Hartree-Fock (mean-field) approach fails to predict the existence of the quasicondensate in the center of the cloud: the quasicondensate is generated by interaction-induced correlations between atoms and not by a saturation of the excited states. Numerical calculations based on Bogoliubov theory give an estimate of the crossover density in agreement with experimental results.
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