Theoretical Studies of the Quantum Hall Effect and Nonlinear Mesoscopic Transport

9632141约翰逊这是一个理论计划，包括两个部分：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，将有丰富的基态和跃迁作为磁场的函数在小量子点的研究，使用以前开发的系综密度泛函方法，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研究分数阶QHE中的非对角长程序和复合费米子的详细性质。 在非线性介观输运，将有一个由PI的和传统的方法，如非平衡绿色的功能与可能的应用，在量子线的二次谐波产生的形式主义的比较研究。 在这两个年轻的PI的支持合作理论研究的补助金中，主要关注两个主题：受到强磁场的电子层的性质，一个被称为量子霍尔效应的主题和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。 ***

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. ***