Mathematical Sciences: Research in the Theory of Disordered Systems (Mathematical Sciences)

克莱因教授是一个强大的小组的领导者， 他是加州大学欧文分校的数学物理学家。 他最近的工作是研究无序系统。 这是对存在下材料性质的研究 杂质 例如，晶体中电子的运动 与杂质的量子力学描述为随机 潜力 最引人注目和极其重要的 具有广泛技术影响的发展，是 材料的电导率显著变化， 杂质 复合材料学复合材料的科学，特别是 半导体在这方面正在经历重大的演变。 无序系统的数学研究，从许多 这一点尤其重要，因为不稳定性往往 干扰自然的物理直觉。 在这一提议中， 克莱因教授将继续他对随机性的富有成效的研究 薛定谔算子和自旋玻璃，特别强调 关于弱无序极限和密度的性质 随机薛定谔算子的状态。

Professor Klein is the leader of a strong group of mathematical physicists at University of California at Irvine. His recent work has been in the study of disordered systems. This is the study of properties of materials in the presence of impurities. For example, the motion of electrons in a crystal with impurities is described quantum mechanically by a random potential. The most striking and exceedingly important development with wide technological implications, is the remarkable change in conductivity of the material due to impurities. The science of composite materials, especially semiconductors, is undergoing a major evolution in this regard. The mathematical study of disordered systems, from many perspectives, is especially important, as instabilities often interfere with the natural physical intuition. In this proposal, Professor Klein will continue his productive study of random Schrodinger operators and spin glasses, with particular emphasis on the weak disorder limit and the properties of the density of states for random Schrodinger operators.