  We consider an exactly soluble model of two Bose-Einstein condensates with a
Josephson-type of coupling. Its equilibrium states are explicitly found showing
condensation and spontaneously broken gauge symmetry. It is proved that the
total number and total phase fluctuation operators, as well as the relative
number and relative current fluctuation operators form both a quantum canonical
pair. The exact relation between the relative current and phase fluctuation
operators is established. Also the dynamics of these operators is solved
showing the collapse and revival phenomenon.
