Exactly Solving Physical Systems: Methods and Applications

精确求解物理系统：方法与应用

• 批准号: 9428-2012
• 负责人: Vinet, Luc
• 金额: $ 1.46万
• 依托单位: Université de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=544640
• 关键词: Exactly; Solving; Physical; Systems; Methods

My research focuses on exactly solving physical models. It bears on the design of systems for the perfect transport of quantum information. It examines quantum walks that are used to develop algorithms for quantum computing. It studies asymmetric exclusion processes that are of relevance in a variety of fields ranging from biopolymerization to traffic flow. It looks also at stochastic processes of interest in genetics modeling. A significant part of my research program is also devoted to systems that are called integrable or superintegrable because they have many conserved quantities. They are theoretically important and have many applications. The underlying methodology is based on the study of symmetries. I am involved in the development of their mathematical description in terms of algebraic structures and orthogonal polynomials and special functions.

我的研究重点是精确求解物理模型。它关系到量子信息完美传输系统的设计。它研究了用于开发量子计算算法的量子行走。它研究了从生物聚合到交通流的各种领域中相关的不对称排斥过程。它还着眼于遗传学建模中感兴趣的随机过程。我的研究计划的一个重要部分也致力于被称为可积或超可积的系统，因为它们有许多守恒量。它们在理论上很重要，并且有很多应用。基本的方法论是基于对称性的研究。我参与发展他们的数学描述方面的代数结构和正交多项式和特殊功能。