  We investigate the phenomenon of decay of a supercurrent in a superconducting
thin film in the absence of an applied magnetic field. The resulting
zero-temperature resistance derives from two equally possible mechanisms: 1)
quantum tunneling of vortices from the edges of the sample; and 2) homogeneous
quantum nucleation of vortex-antivortex pairs in the bulk of the sample,
arising from the instability of the Magnus field's ``vacuum''. We study both
situations in the case where quantum dissipation dominates over the inertia of
the vortices. We find that the vortex tunneling and nucleation rates have a
very rapid dependence on the current density driven through the sample.
Accordingly, whilst normally the superconductor is essentially resistance-free,
for the high current densities that can be reached in high-$T_c$ films a
measurable resistance might develop. We show that edge-tunneling appears
favoured, but the presence of pinning centres and of thermal fluctuations leads
to an enhancement of the nucleation rates. In the case where a periodic pinning
potential is artificially introduced in the sample, we show that
current-oscillations will develop indicating an effect specific to the
nucleation mechanism where the vortex pair-production rate, thus the
resistance, becomes sensitive to the corrugation of the pinning substrate. In
all situations, we give estimates for the observability of the studied
phenomena.
