Mathematical Sciences: Mathematical Problems in Statistical Mechanics and Condensed Matter Physics

首席研究员将讨论统计力学和凝聚态物理的几个不同分支的数学问题。首先，她将研究一些简单经典系统的平衡和非平衡性质。其次，她将研究一些相当简单的量子系统中的集体现象，包括量子自旋模型和具有异常统计的粒子系统。她将处理的所有问题都涉及具有大量自由度的系统的行为，通常是无限的。要发展的数学方法来研究这些系统植根于概率论和分析，但也利用动力系统，微分方程，群论和数值方法。

The principal investigator will address mathematical questions in several different branches of statistical mechanics and condensed matter physics. First, she will investigate both equilibrium and non-equilibrium properties of some simple classical systems. Second, she will study collective phenomena in some rather simple quantum systems, including both quantum spin models and systems of particles with anomalous statistics. All the questions she will address concern the behavior of systems with a large number of degrees of freedom, usually infinite. The mathematical methods to be developed to study these systems are rooted in probability theory and analysis, but also make use of dynamical systems, differential equations, group theory and numerical methods.