New Methods for the Theory of Localization and Directed Wave Propagation

9804983脏电子系统中的Mathur无序效应通常基本上是非微扰的。 虽然一些非微扰的结果是已知的，许多重要的问题仍然存在。 这项理论研究将确定其中一些未回答的问题和相关的方法来研究它们。 第一部分的研究将集中在定向波模型。 从一个角度来看，它可以被解释为一个模型的电子移动在一个嘈杂的晶格（一个与时间相关的随机性）。 统计描述波包在这种介质中的运动的努力已经进行了二十多年。 目前的努力集中在一个完整的统计特性的波包。 在这项研究中，提出了这个问题的解决方案，利用映射，发现由PI，适当的福克-普朗克方程到一个异国情调的铁磁模型。 这个模型可以采用Dyson对普通铁磁体中自旋波的优美分析来分析。 一个详细的解决方案是可取的，因为在定向波模型及其各种应用的内在利益，因为它是类似于统计力学中的噪声动力学的几个重要模型。 定向波模型也描述了量子霍尔多层膜中的输运。 定向波模型的一个特殊版本与一个模型相吻合，该模型非常成功地解释了颗粒材料中的应力传播。 最近的工作稀土金属铁磁体也提供了动机，研究定向波与相关噪声。 将研究与这些系统有关的问题。 第二部分研究静态无序问题。 这里要研究的问题包括介观极限下的电导统计、一维的离域跃迁、脏量子线以及高维的定域和离域。 这些问题中的许多问题长期以来一直无法进行分析。 所使用的方法将是重新解释一个空间维度的时间，从而将一个模型与静态无序的噪声。 脏电子系统中的无序效应通常基本上是非微扰的，例如，不适用于简单的线性技术。 虽然一些非微扰的结果是已知的，许多重要的问题仍然存在。 这项理论研究将确定其中一些未回答的问题和相关的方法来研究它们。 本研究由两部分组成。 在第一种情况下，模拟电子在噪声介质中传播的方程将被转换为类似的磁性模型。 这个模型可以用一种相对简单的方法来求解。 将研究各种其他物理系统的应用。 研究的第二部分将研究电子在无序是静态的材料中的运动。 除了对基础物理学有基本的了解外，这项研究的结果还应该在纳米电子学中得到应用。 ***

9804983 Mathur Disorder effects in dirty electronic systems are often essentially nonperturbative. Although some nonperturbative results are known, many important questions remain. This theoretical research will identify some of these unanswered questions and the associated methods to study them. The first part of the research will focus on the directed wave model. From one point of view it may be interpreted as a model of electrons moving in a noisy lattice (one with time dependent randomness). Efforts to statistically characterize the motion of a wave packet in such a medium have been made for over twenty years. Current efforts focus on a complete statistical characterization of the wave packet. Solutions to this problem are proposed in this research which exploit a mapping, discovered by the PI, of the appropriate Fokker-Planck equation onto an exotic ferromagnetic model. This model can be analyzed by adapting Dyson's beautuful analysis of spin-waves in an ordinary ferromagnet. A detailed solution is desirable because of the intrinsic interest in the directed wave model and its varied applications and because it is similar to several important models of noisy dynamics in statistical mechanics. The directed wave model also describes transport in a quantum Hall multilayer. A special version of the directed wave model coincides with a model that gives a very successful account of stress propagation in granular materials. Recent work on rare-earth metallic ferromagnets also provides motivation to study directed waves with correlated noise. Issues related to these systems will be studied. The second part of the research will focus on problems of static disorder. Here the questions to be studied include the statistics of the conductance in the mesoscopic limit, delocalization transitions in one-dimension, dirty quantum wires, and localization and delocalizations in higher dimensions. Many of these problems have long resisted attempts at analys is. The approach used will be to reinterpret one space dimension as time thereby transforming a model with static disorder to one with noise. %%% Disorder effects in dirty electronic systems are often essentially nonperturbative, e.g., not amenable to simple linear techniques. Although some nonperturbative results are known, many important questions remain. This theoretical research will identify some of these unanswered questions and the associated methods to study them. The research is comprised of two parts. In the first, the equations which model the propagation of an electron in a noisy medium will be transformed to an analogous model of magnetism. This model can then be solved in a relatively straightforward way. Applications to a variety of other physical systems will be studied. The second part of the research will study the motion of electrons in materials for which the disorder is static. Besides yielding a fundamental understanding of the underlying physics, the results of this research should also have applications in nanoelectronics. ***