Decoherence of Bose-Einstein condensates in traps at finite temperature

The phase diffusion of the order parameter of trapped Bose-Einstein condensates at temperatures large compared to the mean trap frequency is determined, which gives the fundamental limit of the line-width of an atom laser. In addition a prediction of the correlation time of the number fluctuations in the condensate is made and related to the phase diffusion via the fluctuation-dissipation relation.