Statistical Mechanics and Dynamics of Disordered Systems

我们将用解析和数值方法研究无序系统的统计力学和动力学。将研究三个主要领域：1)随机环境中的自回避行走，2)氦在多孔介质中的超流转变，3)随机电阻和弹性网络。这些主题将通过各种现代统计力学方法进行研究；包括场论和重整化群、Lifshitz型自变量和数值模拟。这项研究直接关系到理解目前在多孔玻璃中的超流体和凝胶中的聚合物领域的实验。这项工作的第二个基本目标是推动研究无序系统的理论工具的发展。

The statistical mechanics and dynamics of disordered systems will be investigated using analytical and numerical methods. Three major areas will be studied: 1) Self-avoiding walks in random environments, 2) The superfluid transition for Helium in porous media and 3) Random resistor and elastic networks. These topics will be investigated by a variety of modern methods of statistical mechanics; including field theory and the renormalization group, Lifshitz type arguments, and numerical simulation. This research is directly relevant to understanding current experiments in the areas of superfluids in porous glasses and polymers in gels. A second fundamental objective of this work is to advance the development of theoretical tools for the study of disordered systems.