Theoretical Problems in Condensed Matter and Statistical Physics

凝聚态与统计物理的理论问题

• 批准号: 9416910
• 负责人: Bertrand Halperin
• 金额: $ 67万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-11-15 至 2000-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9416910&HistoricalAwards=false
• 关键词: Theoretical; Problems; Condensed; Matter; Statistical

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.

9416910哈珀林研究将集中于凝聚态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。一个主要的问题是准二维电子系统在低温、非常强的磁场中的性质。研究将集中在朗道能级填充分数，在那里没有观察到量子化霍尔效应。理论分析将基于一种数学变换，即电子变成一组费米子，通过虚构的切恩-西蒙斯类型的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Chern-Simons理论适用的基本限制。另一个主要问题将是自旋系统的低温特性，其中量子力学涨落非常重要。其中一个焦点将是高温超导体等材料的性质，这些材料包含具有反铁磁相互作用的准一维自旋一自旋链。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使用复杂几何结构中的各种脉冲序列获得的核磁共振信号的影响。研究将集中在凝聚态和统计物理领域的一系列理论问题上。一个主要的问题将是在低温下，准二维电子层的非常强的磁场中的性质，这种性质出现在各种半导体器件中，如场效应晶体管。这项研究对高温超导体等其他材料也有借鉴意义。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。这项工作可能对采油有一定的应用价值。