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

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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.