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Numerical Methods in Noncommutative Matrix Analysis

非交换矩阵分析中的数值方法

基本信息

批准号：
2110398
负责人：
Terry Loring
金额：
$ 12万
依托单位：
University of New Mexico
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-07-01 至 2024-10-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2110398&HistoricalAwards=false
关键词：
Numerical Methods Noncommutative Matrix Analysis

项目摘要

The project will develop algorithms that are useful for modern physics and quantum information. In particular, the methods developed will be important for modeling topological lasers which are applicable to photonic chips and quantum circuitry. These applications pose challenges to the computational science and in particular to the linear algebra algorithms so they can work with joint measurement in multivariable setting and incommensurate observables recognizing the theoretical limits that exist. The project will consider a variety of multivariable linear algebra algorithms, mainly those filling an immediate need in computational quantum physics and quantum information, but also those that can increase the speed and accuracy of computer shape analysis. The project will involve students and provide training in interdisciplinary projects. This project will develop numerical methods for collections of matrices and operators arising in quantum physics and image analysis. This includes algorithms that work with finite-dimensional approximations to infinite-dimensional systems, leading to better computer modeling of quasicrystals, amorphous systems and periodic systems with defects. Methods and algorithms to be developed will be useful in the study of topological insulators, including periodically-driven systems. The project will study various forms of spectra, including variations of the local density of states, a standard tool in many areas of physics and chemistry. The anticipated work on K-theory is expected to produce new and better tools that can be used by theoretical physicists in numerical studies. At the core of these methods is the study of joint approximate eigenvectors.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.

该项目将开发对现代物理学和量子信息有用的算法。特别是，开发的方法将是重要的建模拓扑激光器，适用于光子芯片和量子电路。这些应用对计算科学，特别是线性代数算法提出了挑战，因此它们可以在多变量设置和不相称的观测量中进行联合测量，从而识别存在的理论极限。该项目将考虑各种多变量线性代数算法，主要是那些满足计算量子物理和量子信息迫切需要的算法，以及那些可以提高计算机形状分析速度和准确性的算法。该项目将让学生参与，并提供跨学科项目的培训。该项目将为量子物理和图像分析中出现的矩阵和算子的集合开发数值方法。这包括与有限维近似无限维系统工作的算法，从而更好地计算机模拟准晶体，无定形系统和周期性系统的缺陷。待开发的方法和算法将有助于拓扑绝缘体的研究，包括磁驱动系统。该项目将研究各种形式的光谱，包括局域态密度的变化，这是物理和化学许多领域的标准工具。对K理论的预期工作预计将产生新的和更好的工具，可供理论物理学家在数值研究中使用。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。