Applied Free Probability Theory

应用自由概率论

• 批准号: 1312831
• 负责人: Alan Edelman
• 金额: $ 10.98万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-01 至 2018-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1312831&HistoricalAwards=false
• 关键词: Applied; Free; Probability; Theory

The goal of this work is to develop and apply modern free probability theory (FPT) to advance understanding of applied problems that traditionally are thought to be too difficult to tackle. The difficulty with quantum many-body systems (QMBS) research is two-fold: 1. The spectra of the sum of local interactions is not easily obtained from the spectra of the summands and 2. The exponential growth with the number of particles of the Hilbert space makes exact diagonalization feeble for any serious study of matter. The nature of the work will be both analytical and computational. The techniques are either entirely unknown to natural scientists or that their potential applicability is obscured by formal presentations. The purpose of this work is to apply an alternative methodology in probability to new physical problems.

这项工作的目标是开发和应用现代自由概率论 (FPT)，以增进对传统上被认为难以解决的应用问题的理解。量子多体系统（QMBS）研究的困难有两个：1. 局域相互作用之和的谱不容易从被加数的谱中获得；2. 局域相互作用的谱随粒子数量的指数增长。希尔伯特空间使得精确的对角化对于任何严肃的物质研究来说都是无力的。这项工作的性质将是分析性的和计算性的。这些技术要么是自然科学家完全不知道的，要么是它们的潜在适用性被正式的介绍所掩盖。 这项工作的目的是将概率的替代方法应用于新的物理问题。