Strongly Correlated Quantum Systems

强相关量子系统

• 批准号: 9113911
• 负责人: Steven Girvin
• 金额: $ 48万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-11-01 至 1995-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9113911&HistoricalAwards=false
• 关键词: Strongly; Correlated; Quantum; Systems

Research will be undertaken on the quantum mechanics of strongly- correlated many-body systems. The objectives are to enhance our understanding of novel phenomena which cannot be addressed by simple perturbation theory. Systems of interest include the integer and fractional quantum Hall effect; transport in mesoscopic devices; the interplay among disorder, interactions and superconductivity in one-dimensional systems; and, the problem of fractional statistics. An important question remaining in the integer quantum Hall effect concerns the nature of Anderson localization in the presence of disorder. The focus of the investigation on the fractional Hall effect will be on the instability to Wigner crystallization in the low filling factor regime and on the nature of edge-state excitations and their role in the transport properties of mesoscopic devices. A central theme of the Hall effect work is the deep and wide-ranging implications of the analyticity of the quantum wave functions in the lowest Landau level. Previous work on the superconductor-insulator transition will be extended to one-dimension and certain exactly soluble models will be investigated. The notions of fractional statistics will be put to practical application in the study of quantum spin systems in two-dimensions.

将对强关联多体系统的量子力学进行研究。其目的是增强我们对新现象的理解，这些现象不是简单的微扰理论所能解决的。感兴趣的系统包括整数和分数量子霍尔效应；介观器件中的输运；一维系统中无序、相互作用和超导电性之间的相互作用；以及分数统计问题。整数量子霍尔效应中的一个重要问题是无序情况下安德森局域化的性质。分数霍尔效应的研究重点将集中在低填充因子区对Wigner结晶的不稳定性，以及边态激发的性质及其在介观器件输运性质中的作用。霍尔效应工作的一个中心主题是最低朗道能级量子波函数的解析性的深刻和广泛的含义。以前关于超导体-绝缘体转变的工作将扩展到一维，并将研究某些精确可解的模型。分数统计的概念将在研究二维量子自旋系统中得到实际应用。