Dynamics and Variational Problems

动力学和变分问题拟议研究的摘要迈克尔·洛斯和埃里克·A·卡伦这个项目将支持对一些数学问题的研究，这些问题是由复杂物理系统的行为问题引起的。我们将开发分析和概率工具来研究统计力学中的一些问题。这些内容包括证明Cercignani猜想的结果，推导最佳几何关联不等式，研究相变研究中出现的某些变分原理，以及量子电动力学中的一些主题。这些结果中的许多都集中在身体动机不平等的证明上。近年来，研究人员使用变分中的技术发现了一些尖锐的几何和解析不等式，并取得了相当大的成功。

Dynamics and Variational ProblemsAbstract of Proposed ResearchMichael Loss and Eric A. Carlen This project will support research on some mathematical problems that are motivated by questions arising from issues about the behavior of complex physical systems. We shall develop analytic and probabilistic tools to study a number of problems in statistical mechanics. These include proving results about Cercignani's conjecture, deriving optimal geometric correlation inequalities, studying certain variational principles that arise in the study of phase transitions and also some topics in Quantum electrodynamics. Many of these results center on the proof of physically motivated inequalities. The investigators have had considerable success in recent years in discovering some sharp geometrical and analytic inequalities using techniques from the calculus of variations.