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

本项目将在 统计领域数学物理 力学和量子力学，重点是影响 猝灭无序和临界现象。 的议题 研究包括：谱性质的运营商与 广泛的疾病，目的是提供一个非- 大于一局部化的微扰求导 三维系统;量子自旋系统的性质 经典自旋模型的随机行走技术 量子传播子的积分表示; 各种模型的临界行为的普遍性。

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.