  We present the quantum phase diagram of mesoscopic SQUID array. We predict
different quan- tum phases and the phase boundaries along with several special
points. We present the results of magnetic flux induced dissipation on these
points and also on the phase boundaries. The Josephson couplings at these
points are dependant on the system parameter in a more complicated fashion and
differ from the Ambegaokar and Baratoff relation. We derive the analytical
relation between the dissipation strength and Luttinger liquid parameter of the
system. We observe some interesting behaviour at the half-integer magnetic flux
quantum and also the importance of co-tunneling effect.
