Transport in Quantum Systems

该奖项将资助无序量子物质的研究，这是一个将物理学、计算机科学和数学联系在一起的跨学科研究领域。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音和缺陷特别敏感。该项目的一个长期目标是了解材料的行为，这些材料可能在创造出对缺陷和噪声具有健壮性的量子计算机方面发挥关键作用。首席研究人员将开发一种基本的数学理论，使人们能够更好地了解这种材料的性质，阐明如何更有效地操纵它们，并利用无序来增强预期结果的稳定性。在理解这类系统的行为方面的进展将增加科学界对理论物理和应用数学模型的理解。参与这个项目的学生将与PI一起工作，并获得该领域的专业知识。该项目将通过一个项目继续进行，以在多体、无序的框架中建立一个自给自足的、系统的运输理论。这个项目的第一个目标是在理解这类系统的时间演化，特别是多体局部化现象及其对(依赖于时间的)扰动的稳健性方面取得实质性进展。这一步需要理解与这个框架相关的准局域性性质，到目前为止，这些性质只在与局域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算符的输运性质，特别是自旋系统。它依赖于构建多体指数理论，该理论在相关系统的流动性间隙区域保持稳定，并依赖于久保的线性响应运输公式的合理性。该奖项反映了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。

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.