Thermodynamics of a trapped Bose gas at low temperature : Departure from the Thomas-Fermi regime.
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We apply the finite temperature Thomas-Fermi (TF) approximation by using the Time dependent Hartree-Fock-Bogoliubov
equations. The exploration of these equations at finite temperature leads to the fact that all the thermodynamics quantities
deviate from the standard values in the TF regime .
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