Systems with Competing Periodicities: Localization and Fractal Fluctuations

9700808萨蒂亚这笔赠款将支持一名女性理论家的工作，她拥有一项国际公认的研究方案，本科生的参与力度很大。这项研究涉及具有竞争长度尺度的系统的性质。这些系统的一个重要方面是存在具有分形特征的奇异相。通过这项工作的大部分工作的概念联系是局部化(和许多与局部化有关的现象)和普遍的分形波动之间的关系。所研究的系统包括呈现动态局域化的量子混沌模型和具有奇怪的非混沌吸引子的经典驱动振子。这些系统将使用PI和她的合作者最近开发的重整化方法进行研究。可能的应用包括表现出巨磁电阻的超晶格的摩擦和磁性的微观模型。%此补助金支持女性PI的理论研究。非线性动力系统的研究涉及复杂的数学技术，本科生和研究生都积极参与。这是一个国际公认的项目的一部分，该项目与来自世界各地的同事长期合作。她的工作应用于目前材料领域的几个活跃领域，包括摩擦的微观模型和磁性超晶格的性质。***

9700808 Satija This grant will support the work of a female theorist who has a research program of international recognition with a strong participation of undergraduate students. The research involves properties of systems with competing length scales. One of the important aspects of these systems is the existence of an exotic phase with fractal characteristics. The conceptual linkage through much of this work is the relationship between localization (and many phenomena related to localization) and the universal Fractal fluctuations. The proposed systems under investigation include quantum chaos models exhibiting dynamical localization and classical driven oscillators with strange non-chaotic attractors. These systems will be studied by using a renormalization methodology developed recently by the PI and her collaborators. The possible applications include a microscopic model of friction and magnetic properties of superlattices exhibiting giant magnetoresistance. %%% This grant supports theoretical research of a female PI. The research on nonlinear dynamical systems involves sophisticated mathematical techniques with active participation by undergraduate and graduate students. It is part of an internationally recognized program with long- standing collaborations with colleagues from around the world. Her work has applications to several currently active areas in materials; including microscopic models of friction and properties of magnetic superlattices. ***