Quantum Fluctuations and Superconductivity in Granular Films and Josephson Junctions.

A theory of a universal normal state resistance criterion for the onset of superconductivity in ultra-small Josephson arrays, and in granular films modeled by such arrays, is described. The mean field theory of the quantum Cooper pair phase fluctuation driven transition is applied to the calculation of the normal state resistance and bias current dependence of the AC response of the globally superconducting state. A first correction to the mean field zero temperature threshold is computed using the Bethe approximation.