Eur. Phys. J. D 59, 427-434 (2010)
https://doi.org/10.1140/epjd/e2010-00177-5

Variational self-consistent theory for trapped Bose gases at finite temperature

Laboratory for Theoretical Physics and Material Physics, Faculty of Sciences and Engineering Sciences, Hassiba Benbouali University of Chlef, B.P. 151, 02000, Chlef, Algeria

Corresponding author: ^a benarous_med@yahoo.fr

Received: 22 January 2010
Revised: 31 March 2010
Published online: 29 June 2010

Abstract

We apply the time-dependent variational principle of Balian-Vénéroni to a system of self-interacting trapped bosons at finite temperature. The method leads to a set of coupled non-linear time dependent equations for the condensate density, the thermal cloud and the anomalous density. We solve numerically these equations in the static case for a harmonic trap. We analyze the various densities as functions of the radial distance and the temperature. We find an overall good qualitative agreement with recent experiments as well as with the results of many theoretical groups. We also discuss the behavior of the anomalous density at low temperatures owing to its importance to account for many-body effects.