Mathematical Sciences: Research in Phenomena Occurring in Disordered Systems and in Statistical Mechanics

克莱因将研究发生在无序系统中的现象。主题包括随机环境下的量子自旋系统、随机环境下的接触和渗透过程、随机薛定谔算子和经典转子的临界指数。Shlosman将研究统计力学中低温随机场的性质。这些场的多相结构反映在它们的大偏差概率的不寻常性质上，这是由于在典型的大偏差构型中形成不同相的晶体的现象。现代物理学，量子力学和相对论，是二十世纪的产物。它牢固地建立在上个世纪对物质微观结构的研究和对超距作用、电磁和热辐射等概念的理解上。这些发展的数学基础，统称为数学物理学，范围从控制粒子动力学的薛定谔算子的详细分析，到试图将四种已知力统一为单一理论的统一场论。

Klein will study phenomena that occur in disordered systems. The topics included are quantum spin systems in a random environment, contact and percolation processes in a random environment, random Schroedinger operators, and critical exponents for classical rotors. Shlosman will investigate properties of low temperature random fields in statistical mechanics. The multiphase structure of these fields is reflected in the unusual properties of their large deviations probabilities, due to the phenomenon of formation of crystals of different phases in typical large deviation configurations. Modern physics, quantum mechanics and relativity, is a product of the twentieth century. It is founded firmly in the last century's attempt to address the microstructure of matter and to come to grips with the concepts of action-at-a distance, electro-magnetism, and heat radiation. The mathematical foundations for these developments, collectively called mathematical physics, ranges from detailed analysis of Schroedinger operators, which governs the dynamics of particles, to unified field theory, which attempts to unite the four known forces into a single theory.