Quantum Critical Phenomena in Disordered Interacting Bose Systems

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The physics of disordered, correlated Bose sytems constitutes a major challenge. Recently a density controlled superfluid transition was observed in helium-four absorbed in porous materials with a superfluid density exponent contrdicting earlier theories; new types of scaling behavior of the resistivity have been seen in disordered superconducting films and wires; and the observation of a possible universal conductance in granular superconducting films has attracted considerable excitement. A related problem of primary importance is the vortex state of the high temperature superconductors, where an unconventional, vortex-glass phase has been observed in some materials. At the same time, the discovery of heavy fermion and oxide superconductors has driven a substantial improvement in numerical techniques and also led to genuinely new analytical approaches to strongly correlated fermions. These advanceshave yet to be applied to the interacting boson problem. The research will apply Quantum Monte Carlo, the Schwinger boson approach and the perturbative scaling methids of localization theory to explore the quantum phase transitions taking place in helium-four absorbed in porous media and granular superconductors, as modeled by a disordered, interacting boson Hamiltonian. The disorder will be handled by methods which were successful in the spin-glass problem, among others finite size scaling of appropriately chosen dimensionless quantities, and a suitable version of the maximum entropy method. %%% Theoretical research will be conducted using numerical and analytical techniques to study the behavior of disordered, interacting many particle systems which obey Bose statistics. New methods will be applied to describe such diverse physical systems as properties of helium absorbed in porous materials and the behavior of high temperature superconductors.