  In the absence of losses the phase of a Bose-Einstein condensate undergoes
collapses and revivals in time due to elastic atomic interactions. As
experiments necessarily involve inelastic collisions, we develop a model to
describe the phase dynamics of the condensates in presence of collisional
losses. We find that a few inelastic processes are sufficient to damp the
revivals of the phase. For this reason the observability of phase revivals for
present experimental conditions is limited to condensates with a few hundreds
of atoms.
