We study bilayer quantum Hall systems at total Landau level filling factor
ν=1 in the presence of interlayer tunneling and coupling to a dissipative
normal fluid. Describing the dynamics of the interlayer phase by an effective
quantum dissipative XY model, we show that there exists a critical dissipation
σc set by the conductance of the normal fluid. For σ>σc,
interlayer tunnel splitting drives the system to a ν=1 quantum Hall state.
For σ<σc, interlayer tunneling is irrelevant at low temperatures,
the system exhibits a superfluid transition to a collective quantum Hall state
supported by spontaneous interlayer phase coherence. The resulting phase
structure and the behavior of the in-plane and tunneling currents are studied
in connection to experiments.Comment: 4 RevTex pages, revised version, to appear in Phys. Rev. Let