On the Thomas-Fermi approximation in the bulk of trapped Bose-Einstein condensed gases

Corrections to the Thomas-Fermi-type solution of the Gross-Pitaevskii equation are inevitable in order to get correctly the frequencies of the low lying modes out of the Bogolyubov equations. These corrections are important in the bulk, too, thus the failure of the Thomas-Fermi approximation is not confined to the surface. We discuss this effect quantitatively and consider similar phenomena of spin fluctuations in Bose-Einstein condensed gases in an optical trap.