Theoretical Studies of the Quantum Hall Effect and Nonlinear Mesoscopic Transport

量子霍尔效应与非线性介观输运的理论研究

• 批准号: 9632141
• 负责人: Michael Johnson
• 金额: $ 18万
• 依托单位: The University of Central Florida Board of Trustees
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-15 至 2000-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9632141&HistoricalAwards=false
• 关键词: Theoretical; Studies; Quantum; Hall; Effect

9632141 Johnson This is a theoretical program consisting of two parts: to study the fundamental properties of integer and fractional quantum Hall effect (QHE) and to study nonlinear mesoscopic transport. More specifically, in the first part there will be a study of the rich ground states and transitions as a function of magnetic field in small quantum dots, using a previously developed ensemble density functional method which will be extended to include spin degrees of freedom and current distributions. Further applications of this method include a study of the off-diagonal long range order in the fractional QHE and detailed properties of the composite fermion. In the nonlinear mesoscopic transport, there will be a comparative study of a formalism developed by the PI's and the traditional approaches such as nonequilibrium Green's function with possible application to the second harmonic generation in quantum wires. %%% In this grant supporting collaborative theoretical research by the two young PI's, the main focus is on two subjects: properties of layers of electrons subjected to intense magnetic fields, a subject referred to as quantum Hall effect and on response of small devices to intense radiation. Both of these projects involve special theoretical techniques developed by these PI's. ***

这是一个由两部分组成的理论计划：研究整数和分数量子霍尔效应（QHE）的基本性质和研究非线性介观输运。更具体地说，在第一部分中，将使用先前开发的集合密度泛函方法研究小量子点中丰富的基态和跃迁作为磁场的函数，该方法将扩展到包括自旋自由度和电流分布。该方法的进一步应用包括分数阶QHE的非对角长阶和复合费米子的详细性质的研究。在非线性介观输运中，将会比较PI发展的形式主义和传统的方法，如非平衡格林函数，以及可能应用于量子线中二次谐波产生的可能性。在这项支持两位年轻的PI合作理论研究的资助中，主要关注两个主题：受强磁场影响的电子层的性质，一个主题被称为量子霍尔效应，以及小型设备对强辐射的响应。这两个项目都涉及这些PI开发的特殊理论技术。＊＊＊