  We report on the reinforcement of superconductivity in a system consisting of
a narrow superconducting wire weakly coupled to a diffusive metallic film. We
analyze the effective phase-only action of the system by a perturbative
renormalization-group and a self-consistent variational approach to obtain the
critical points and phases at T=0. We predict a quantum phase transition
towards a superconducting phase with long-range order as a function of the wire
stiffness and coupling to the metal. We discuss implications for the DC
resistivity of the wire.
