A theoretical analysis is presented of the problem of the onset of global phase coherence in granular superconductors and Josephson-junction arrays. It is shown that the ratio $\frac{\left(\frac{h}{e^2}\right)}{R}$, where $R$ is the resistance, plays an important role in the thermodynamics. This is due to quantum fluctuations of the order parameter and occurs in superconductivity only because the phase of the order parameter is both a statistical as well as a dynamical variable. The theory provides a natural qualitative explanation of the recent experiments of Orr, Jaeger, Goldman, and Kuper.

• Received 11 February 1986

DOI:https://doi.org/10.1103/PhysRevLett.56.2303