  Within the classical field model, we find that the phase of a Bose-Einstein
condensate undergoes a true diffusive motion in the microcanonical ensemble,
the variance of the condensate phase change between time zero and time $t$
growing linearly in $t$. The phase diffusion coefficient obeys a simple scaling
law in the double thermodynamic and Bogoliubov limit. We construct an
approximate calculation of the diffusion coefficient, in fair agreement with
the numerical results over the considered temperature range, and we extend this
approximate calculation to the quantum field.
