A mesoscopic Josephson junction in a superconducting ring enclosing a magne
tostatic flux with dissipation is considered. The dissipation in this syste
m is described as a consequence of its coupling to a reservoir. By solving
the master equation it is shown that the state of the junction can evolve i
nto a quantum superposition of two coherent states even when the dissipatio
n is present. It is also shown that squeezing effects can exist in such a s
ystem, and the dynamic behavior of the supercurrent shows collapse and revi
val phenomena. The quantum decoherence is also discussed.