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RAISE-TAQS: The Hidden Structure of the Disorder in Quantum Systems

RAISE-TAQS：量子系统中无序的隐藏结构

基本信息

批准号：
1839077
负责人：
Svitlana Mayboroda
金额：
$ 100万
依托单位：
University of Minnesota-Twin Cities
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-09-15 至 2024-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1839077&HistoricalAwards=false
关键词：
RAISE TAQS Hidden Structure Disorder

项目摘要

This is an interdisciplinary program at the interface of mathematics, quantum semiconductor physics, and the material science of GaN semiconductors, devoted to the rigorous understanding and control of the disordered systems with the aim to grant the power to design, beyond just observing, new quantum objects hidden in disordered semiconductor materials. A program of theoretical and experimental research will be launched which pioneers the use of localized states in disordered semiconductor alloys as quantum dots and offers breakthrough achievements across several related areas which range from mathematics of the disordered systems, to quantum physics, to nanoscale materials design and characterization. The grand goal of this project is to predict and manipulate localization properties of electron matter waves in disordered media in precise, quantifiable, mathematical terms, with the applications to novel well-behaved quantum objects in the localization regions of semiconductor alloys.Specifically, in mathematics, the project aims at the first deterministic theory revealing the precise geometric structure of waves and more general solutions to PDEs in the presence of disorder. The first treatment of localization in Poisson-Schrodinger and similar self-consistent systems, and the first treatment of localization by geometry, and a complete resolution of the problem of absolute continuity of elliptic measure. In experimental material science, the project aims at the inauguration of the field of localization engineering, including designing self-occurring nanostructures, based on the InGaN materials system of LEDs, with desired properties based on the control of electron localization at the microscopic scale, optimization of their exciton properties, control of the transport between the localized states, their relaxation and coherence times. In physics, the goal is a new approach to quantum effects in disordered systems, with the emphasis on the outstanding open problems of decoherence in quantized semiconductor structures. At stake is the demonstration that disorder can greatly improve quantum parameters such as the coherence time, which is the first mandatory step for building stable entangled state generators.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.

这是一个将数学、量子半导体物理和GaN半导体材料科学结合在一起的交叉学科计划，致力于严格理解和控制无序系统，目的是赋予设计能力，而不仅仅是观察，隐藏在无序半导体材料中的新量子物体。将启动一项理论和实验研究计划，开创将无序半导体合金中的局域态用作量子点的先河，并在从无序系统数学到量子物理再到纳米材料设计和表征的几个相关领域取得突破性成果。这个项目的宏伟目标是用精确的、可量化的数学术语来预测和操纵无序介质中电子物质波的局域化性质，并将其应用于半导体合金局域区的新型良好量子对象。具体地说，在数学上，该项目旨在研究第一个确定性理论，揭示波的精确几何结构和无序情况下偏微分方程组的更一般的解。第一次处理Poisson-Schrodinger和类似自洽系统的局部化，第一次用几何处理局部化，完全解决了椭圆测度的绝对连续性问题。在实验材料科学领域，该项目旨在开创局域化工程领域的先河，包括基于LED的InGaN材料系统设计自产生的纳米结构，具有期望的性质，其基础是在微观尺度上控制电子局域化，优化其激子性质，控制局域态之间的传输，它们的驰豫和相干时间。在物理学中，目标是一种新的方法来研究无序系统中的量子效应，重点是量子化半导体结构中尚未解决的退相干问题。关键是证明无序可以极大地改善量子参数，如相干时间，这是建立稳定的纠缠态生成器的第一个强制性步骤。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。