Quantum Critical Phenomena in Disordered Interacting Bose Systems

无序的、关联的玻色系统的物理学构成了一个重大挑战。最近，在吸附在多孔材料中的氦-4中观察到了一种密度控制的超流转变，其超流密度指数与以前的理论相反；在无序超导薄膜和导线中观察到了新类型的电阻率标度行为；在颗粒超导薄膜中观察到可能的普遍电导引起了相当大的兴奋。一个最重要的相关问题是高温超导体的涡旋态，在某些材料中观察到了非常规的涡旋玻璃相。与此同时，重费米子和氧化物超导体的发现推动了数值技术的实质性改进，也导致了对强关联费米子的真正新的分析方法。这些进展还没有应用于相互作用的玻色子问题。这项研究将应用量子蒙特卡罗、Schwinger玻色子方法和局域化理论的微扰标度方法来研究吸附在多孔介质和颗粒超导体中的氦-4原子发生的量子相变，其模型为无序的相互作用玻色子哈密顿量。这种无序将通过在自旋玻璃问题中取得成功的方法来处理，其中包括适当选择无量纲量的有限尺寸标度，以及最大熵方法的适当版本。理论研究将使用数值和分析技术来研究无序的、相互作用的多粒子系统的行为，这些粒子系统服从玻色统计。新的方法将被用来描述不同的物理系统，如多孔材料中吸附的氦的性质和高温超导体的行为。

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.