Theoretical Studies of Classical and Quantum Coherent Vortex States in Arrays of Mesoscopic Superconductors

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9521845 Jose A variety of systems will be investigated theoretically which impact modern condensed matter physics. Problems to be studied relate to glassy behavior in superconductors, macroscopic quantum coherent phenomena, superconductor- insulator transitions, and coherent oscillatory vortex patterns. These problems can be studied experimentally in a unique OcleanO way in artificially fabricated Josephson junction arrays. Different types of collective vortex ordering in these arrays will be investigated both in the classical and, mostly, in the quantum regime. The dynamic response of Josephson junction arrays will be modeled by a Langevin equation for the phases of the superconducting order parameter and by MaxwellOs equations for the self- induced fields. Research will also be extended on the response of mesoscopic systems with specially designed geometries that have chaotic solutions in the classsical limit. These theoretical problems are motivated by experiments and by the desire to expand our understanding of previous theoretical predictions for the existence of novel coherent vortex states. The theoretical techniques to be used include large scale classical and quantum Monte Carlo simulations, renormalization group techniques, classical dynamical systems theory, many-body techniques, path integral methods, pseudo-spectral methods, and other theoretical approaches deemed necessary. Algorithms will be developed for serial, vector and parallel platforms. The results of this study are likely to impact the field of quantum effect electronics. %%% A theoretical and computational study will be made of strongly interactiong microelectronic arrays. These arrays are excellent models for a variety of physical systems including high temperature superconductors. They also exhibit chaotic behavior in certain regimes. Besides possessing model behavior, these arrays also serve as actual devices which incorporate quantum effects at the microelectronic scal e. ***