  We analyze a process of splitting of the Bose-Einstein condensate and the
mutual coherence of two separated atomic clouds. Within the classical fields
approximation we show that coherence between clouds is degraded if atoms
interact and if we account for the sufficiently long observation time. We also
show, that upon recombination, the coherence across the sample is restored. The
coherence is not fully degraded if the splitting potential remains sufficiently
penetrable. We calculate the variance of atom number difference for this
time-averaging measurement and show that for low temperatures it can be well
below Poissonian limit like it was observed in the experiments.
