This research will rely heavily on the use of (supercomputer) numerical as well as analytic techniques to study the properties of homogeneous and inhomogeneous superconductors. The theoretical techniques include: Quantum Monte Carlo simulations, renormalization group theory, dynamical systems theory, many body theory, path integral methods and any other theoretical approach that may be deemed necessary to unravel the physics of interest. The problems to be considered motivate and are motivated directly by experimental findings in low and high temperature superconductors. Specifically, the effects of quantum zero point fluctuations, magnetic fields, dissipation and disorder in arrays of ultrasmall superconductor networks. Also, we propose to carry out a direct comparison of the physical sources of metastability in the magnetic properties predicted to appear in artificially fabricated random arrays of Josephson junctions and those found in the novel high temperature oxide superconductors. The physics that will emerge from the work proposed here could have an impact in the understanding of the submicron structures that promise to lead to a new type of quantum effect electronic devices.
