Transport in Quantum Systems

量子系统中的传输

• 批准号: 2307093
• 负责人: Alexander Elgart
• 金额: $ 20万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2307093&HistoricalAwards=false
• 关键词: Transport; Quantum; Systems

This award will fund research on disordered quantum matter, an interdisciplinary research area interlinking physics, computer science, and mathematics. Disorder is an inherited feature of any physical system, but the miniaturization of physical devices makes them especially sensitive to noise and imperfections. A longstanding goal of this project is to understand the behavior of materials that could play a crucial role in creating quantum computers robust to defects and noise. The principal investigator will develop an underlying mathematical theory that will allow for a better understanding of the properties of such materials, shed light on how to manipulate them more effectively, and harness disorder to enhance the stability of the desired outcomes. Progress in understanding the behavior of such systems will increase the scientific community's understanding of models in theoretical physics and applied mathematics. Students involved in this project will work alongside the PI and gain expertise in the area.The project will proceed through a program to build a self-contained, systematic transport theory in the many-body, disordered framework. The first goal of this project is to make substantial progress in understanding the time evolution of such systems, particularly the many-body localization phenomenon and its robustness to (time-dependent) perturbations. This step requires understanding the quasi-locality properties associated with this framework, which have so far been obtained only in the context of the gapped ground states associated with local Hamiltonians. The project's second goal is the analysis of the transport properties of disordered many-body Hamiltonians, particularly spin systems. It relies on constructing a many-body index theory that remains stable in a mobility gap region of the associated system and on the justification of Kubo's transport formulae for the linear response.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.

该奖项将资助无序量子物质的研究，这是一个将物理学、计算机科学和数学相互联系的跨学科研究领域。无序是任何物理系统的遗传特征，但物理设备的小型化使它们对噪声和缺陷特别敏感。该项目的长期目标是了解材料的行为，这些材料在创建对缺陷和噪声具有鲁棒性的量子计算机方面发挥着至关重要的作用。首席研究员将开发一种基础数学理论，使人们能够更好地理解此类材料的特性，阐明如何更有效地操纵它们，并利用无序性来增强所需结果的稳定性。对此类系统行为的理解取得的进展将增加科学界对理论物理和应用数学模型的理解。参与该项目的学生将与 PI 一起工作并获得该领域的专业知识。该项目将通过一项计划进行，以在多体、无序的框架中建立一个独立的、系统的运输理论。该项目的首要目标是在理解此类系统的时间演化方面取得实质性进展，特别是多体定位现象及其对（时间相关）扰动的鲁棒性。此步骤需要了解与该框架相关的准局域性质，迄今为止，这些性质仅在与局部哈密顿量相关的有隙基态的背景下获得。该项目的第二个目标是分析无序多体哈密顿量的输运特性，特别是自旋系统。它依赖于构建在相关系统的移动间隙区域中保持稳定的多体指数理论，以及久保线性响应输运公式的合理性。该奖项反映了 NSF 的法定使命，并通过评估被认为值得支持利用基金会的智力优势和更广泛的影响审查标准。