Localization and Diffusion in Open and Many Body Quantum Systems

开放多体量子系统中的局域化和扩散

基本信息

批准号：
1900015
负责人：
Jeffrey Schenker
金额：
$ 25万
依托单位：
Michigan State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-08-01 至 2022-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1900015&HistoricalAwards=false
关键词：
Localization Diffusion Open Many Body

项目摘要

The main focus of this project is the study of the effects of disorder on quantum systems. In a broader context, the work draws inspiration from the basic scientific question: "What are the effects of disorder?" This is a fundamental question relevant to any scientific model, even one in which disorder is not explicitly included. After all, any real world system is subject to a small amount of noise, and experience shows that even weak disorder may have a profound effect on the behavior of the system. The equations studied in this project arise in the theory of disordered materials, but are of general interest because of the fundamental nature of both wave motion and disorder. Progress in understanding the solutions to these equations will improve basic understanding of models of theoretical physics and applied mathematics. In addition, a central goal of the research is pedagogical: to introduce students to a fundamental subject and convey to them that mathematical and theoretical physics are vibrant, growing fields. The project will proceed through a program of research on the effects of disorder in physical models. The main focus of the research is in understanding the evolution of quantum systems subject to intrinsic disorder. When disorder is weak, the expectation is that a diffusive evolution of the wave function results. At stronger disorder, it is known that localization of the wave function can occur, although the exact nature of localization in many body and open quantum systems is poorly understood. Two key goals are 1) to analyze the diffusion of waves in a weakly disordered medium over arbitrarily long times, and 2) to clarify the nature of localization in many body models. In recent years the PI and various post-doc and student collaborators have considered the problem of wave diffusion in time-dependent random media, with the time dependence generated by a Markov process. For such models the diffusive propagation, e.g., for the tight binding Schrodinger equation, can be established by spectral analysis. One aim of the present project is to approach the time independent equation as a perturbation of these time dependent equations, which have the virtue of sharing the expected qualitative behavior. In parallel, we will study disorder induced localization in polaron type models of a interacting systems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目的主要重点是研究疾病对量子系统的影响。在更广泛的背景下，这项工作从基本科学问题中汲取了灵感：“疾病的影响是什么？”这是与任何科学模型相关的基本问题，即使是疾病未明确包括的模型。毕竟，任何现实世界系统都会遇到少量噪音，并且经验表明，即使是弱的疾病也可能对系统的行为产生深远的影响。该项目中研究的方程式出现在无序材料理论中，但由于波动和混乱的基本性质而引起了人们的普遍关注。了解这些方程的解决方案的进展将改善对理论物理和应用数学模型的基本理解。此外，该研究的一个核心目标是教学：向学生介绍一个基本学科，并向他们传达数学和理论物理学是充满活力的成长领域。该项目将通过有关物理模型中疾病影响的研究计划进行。该研究的主要重点是理解受内在障碍的量子系统的演变。当疾病较弱时，期望是波函数的扩散演变。在更强的疾病下，尽管对许多身体和开放量子系统的定位的确切性质的确切性质却很少，但已知波功能的定位可能会发生。两个关键目标是1）分析任意长时间的弱无序培养基中波的扩散，以及2）阐明许多人体模型中定位的性质。近年来，PI和各种博士后和学生合作者考虑了时间依赖的随机介质的波扩散问题，而Markov过程产生了时间依赖性。对于此类模型，可以通过光谱分析来建立扩散的传播，例如，对于紧密的结合施罗宾格方程。本项目的目的之一是将时间独立方程式作为这些时间依赖方程的扰动，这具有共享预期的定性行为的优点。同时，我们将研究障碍在相互作用系统的极性类型模型中引起的本地化。该奖项反映了NSF的法定任务，并被认为是使用基金会的知识分子优点和更广泛的影响评估标准来通过评估来获得支持的。