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

• 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

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.

这是数学，量子半导体物理学和GAN半导体的材料科学的界面的跨学科计划，致力于对无序系统的严格理解和控制，旨在赋予设计的能力，仅仅观察到隐藏在无序的半导体材料中的新量子。 将启动一项理论和实验研究计划，开创局部半导体合金中的局部状态作为量子点，并在几个相关领域提供突破性成就，这些领域的突破性成就从无序系统的数学到量子物理学到量子物理学到纳米级材料的设计和表征。 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. 在泊松雪松和类似的自洽系统中对定位的首次处理，以及通过几何形状对定位的首次处理，以及完全解决椭圆度度量绝对连续性问题的完全解决。 在实验材料科学中，该项目旨在基于INGAN材料系统制定本地化工程领域的开幕典礼，包括设计自我发生的纳米结构，并基于在微观量表上对电子定位的控制，优化其兴奋性特性的电子定位，对本地化状态的运输，控制其本地化状态，并将其放松时代的运输。 在物理学中，目标是一种在无序系统中的量子效应的新方法，重点是量化半导体结构中的不良开放问题。危险的证明是，疾病可以大大改善量子参数，例如连贯性时间，这是建造稳定的纠缠状态发电机的第一步。该奖项反映了NSF的法定任务，并被认为是通过基金会的知识分子优点和更广泛的审查标准来评估值得通过评估来支持的。

项目成果

The effective potential of an M -matrix

M 矩阵的有效势

• DOI: 10.1063/5.0042629
• 发表时间: 2021
• 期刊: Journal of Mathematical Physics
• 影响因子: 1.3
• 作者: Filoche, Marcel;Mayboroda, Svitlana;Tao, Terence
• 通讯作者: Tao, Terence

The Landscape Law for Tight Binding Hamiltonians

紧束缚哈密顿量的景观定律

• DOI: 10.1007/s00220-022-04494-8
• 发表时间: 2022
• 期刊: Communications in Mathematical Physics
• 影响因子: 2.4
• 作者: Arnold, Douglas;Filoche, Marcel;Mayboroda, Svitlana;Wang, Wei;Zhang, Shiwen
• 通讯作者: Zhang, Shiwen

Critical perturbations for second-order elliptic operators, I: Square function bounds for layer potentials

二阶椭圆算子的临界扰动，I：层势的平方函数界限

• DOI: 10.2140/apde.2022.15.1215
• 发表时间: 2022
• 期刊: Analysis & PDE
• 影响因子: 2.2
• 作者: Bortz, Simon;Hofmann, Steve;Luna García, José Luis;Mayboroda, Svitlana;Poggi, Bruno
• 通讯作者: Poggi, Bruno

Sharp estimates for the integrated density of states in Anderson tight-binding models

安德森紧束缚模型中积分态密度的锐估计

• DOI: 10.1103/physreva.104.012207
• 发表时间: 2021
• 期刊: Physical Review A
• 影响因子: 2.9
• 作者: Desforges, Perceval;Mayboroda, Svitlana;Zhang, Shiwen;David, Guy;Arnold, Douglas N.;Wang, Wei;Filoche, Marcel
• 通讯作者: Filoche, Marcel

Impact of doped barriers on the recombination coefficients of c -plane InGaN/GaN single quantum well light-emitting diodes

掺杂势垒对c面InGaN/GaN单量子阱发光二极管复合系数的影响

• DOI: 10.1063/5.0117318
• 发表时间: 2022
• 期刊: Applied Physics Letters
• 影响因子: 4
• 作者: Chow, Y. C.;Lynsky, C.;Nakamura, S.;DenBaars, S. P.;Weisbuch, C.;Speck, J. S.
• 通讯作者: Speck, J. S.