"Integrable Systems, Random Matrices and Random Processes"

“可积系统、随机矩阵和随机过程”

• 批准号: 45858-2012
• 负责人: Harnad, John
• 金额: $ 1.46万
• 依托单位: Concordia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=507301
• 关键词: Integrable; Systems; Random; Matrices; Processes

The range of areas to which the theory of classical and quantum integrable systems is applicable has been rapidly growing since the break-through discovery of the inverse scattering method within the field of soliton physics in the late 1960's. These now include such diverse applications as: the spectral theory of random matrices; integrable random processes, such as "exclusion" processes, crystal and polymer growth, and the remarkable "integrability" properties discovered recently in gauge field theory, governing the fundamental interactions of matter. The problems addressed in this proposal touch upon all these fields.

自从20世纪60年代末在孤子物理学领域内突破性地发现逆散射方法以来，经典和量子可积系统理论适用的领域范围迅速扩大。这些现在包括这样不同的应用：随机矩阵的谱理论;可积随机过程，如“排斥”过程，晶体和聚合物生长，以及最近在规范场论中发现的显着的“可积性”性质，支配物质的基本相互作用。这一建议所涉及的问题涉及所有这些领域。