Theoretical Problems in Condensed Matter and Statistical Physics

9416910 Halperin Research将专注于凝聚态物质和统计物理领域的一系列理论问题。长期目标是提高对强相互作用多体系统和高度无序材料的基本理解，发展新的理论和计算技术，并解释突出的实验难题。一个主要的关注将是准二维电子系统在低温下的性质，在非常强的磁场。研究将集中在朗道能级填充分数，其中量化霍尔效应没有被观察到。理论分析将基于一种数学转换，在这种转换中，电子变成一组费米子，通过一个虚构的陈-西蒙斯型电场和磁场相互作用。要研究的课题包括有限温度输运实验，以及费米子陈-西蒙斯理论适用性的基本限制。另一个主要的问题是自旋系统的低温特性，其中量子力学涨落是非常重要的。一个焦点将是材料的性质，如高温超导体，包含具有反铁磁相互作用的准一维自旋-自旋链。其他工作将探索具有受挫相互作用的高维自旋系统。其他研究将包括无序系统的性质，特别是对岩石等多孔介质中水的核磁共振研究。这里的重点将是分析水分子的扩散对核磁共振信号的影响，这些核磁共振信号是使用复杂几何形状的各种脉冲序列获得的。研究将集中在凝聚态和统计物理领域的一系列理论问题。一个主要的关注将是在低温下的性质，在非常强的磁场中的准二维电子层，发生在各种半导体器件，如场效应晶体管。这项研究对其他材料如高温超导体也有启示意义。其他研究将包括无序系统的性质，特别是对岩石等多孔介质中水的核磁共振研究。这项工作可能应用于石油开采。

9416910 Halperin Research will focus on a range of theoretical problems in the field of condensed matter and statistical physics. Long-range goals are to improve the basic understanding of strongly interacting many- body systems and highly disordered materials, to develop new theoretical and computational techniques, and to explain outstanding experimental puzzles. A major concern will be properties of quasi-two-dimensional electron systems at low temperatures, in very strong magnetic fields. Research will concentrate on Landau-level filling fractions where the quantised Hall effect is not observed. Theoretical analysis will be based on a mathematical transformation where the electrons become a set of fermions that interact through a fictitous electric and magnetic field of the Chern-Simons type. Topics to be studied include finite temperature transport experiments, as well as fundamental limits to the applicability of the fermion Chern-Simons theory. Another major concern will be low-temperature properties of spin systems where quantum mechanical fluctuations are very important. One focus will be properties of materials such as high temperature superconductors which contain quasi-one-dimensional spin-one spin chains with antiferromagnetic interactions. Other work will explore higher dimensional spin systems with frustrated interactions. Other research will include properties of disordered systems, especially nuclear magnetic resonance studies of water in porous media such as rocks. The focus here will be the analysis of the effects of the diffusion of water molecules on nuclear magnetic resonance signals obtained using various pulse sequences in complex geometries. %%% Research will focus on a range of theoretical problems in the field of condensed matter and statistical physics. A major concern will be properties at low temperatures, in very strong magnetic fields of quasi-two-dimensional electron layers, which occur in various semiconductor devices such as the field-effect transistor. The research also has implications for other materials such as high- temperature superconductors. Other research will include properties of disordered systems, especially nuclear magnetic resonance studies of water in porous media such as rocks. This work may have application to oil recovery.