Disorder Effects and Critical Behavior in Statistical Mechanics and in Quantum Systems

本项目将在统计力学和量子力学领域开展数学物理基础研究，重点研究淬火失序和临界现象的影响。要研究的主题包括：具有广泛无序的算子的谱性质，目的是提供高维系统中局部化的非微扰推导；利用经典自旋模型中的随机游走技术研究量子自旋系统在量子传播子路径积分表示中的性质各种模型临界行为的普适性证明。

This project will carry out basic research in mathematical physics on topics in the area of statistical mechanics and quantum mechanics with emphasis on the effects of quenched disorder and critical phenomena. The topics to be studied include: spectral properties of operators with extensive disorder with the aim of providing a non- perturbative derivation of localization in higher-than-one dimensional systems; properties of quantum spin systems using random-walk techniques from classical spin models in the path integral representation of the quantum propagators; proofs of universality in the critical behavior for a variety of models.