Toroidal quantum groups, integrable models and applications

环形量子群、可积模型和应用

• 批准号: DE210101264
• 负责人: Dr Alexandr Garbali
• 金额: $ 24.08万
• 依托单位: The University of Melbourne
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2021
• 资助国家: 澳大利亚
• 起止时间: 2021-02-01 至 2024-03-05
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE210101264
• 关键词: Toroidal; quantum; groups; integrable; models

Modelling systems of quantum and classical mechanics usually relies on computationally expensive numerical methods. Such methods typically provide raw answers and give little insight. In contrast, a special class of modelling based on quantum integrability provides us with a variety of analytic tools thanks to connections with algebra, geometry and combinatorics. The project aims to study quantum integrability with the help of new exciting developments in toroidal quantum groups. The anticipated outcomes include constructions of new models, developing analytic methods and computer algebra packages. These results are expected to facilitate challenging computational problems in modelling of quantum and classical systems.

量子力学和经典力学的建模系统通常依赖于计算昂贵的数值方法。这些方法通常提供原始答案，并提供很少的见解。相比之下，基于量子可积性的一类特殊建模为我们提供了各种分析工具，这要归功于与代数，几何和组合学的联系。该项目的目的是研究量子可积性的帮助下，新的令人兴奋的发展，在环形量子群。预期成果包括新模型的构建，开发分析方法和计算机代数软件包。这些结果有望促进量子和经典系统建模中具有挑战性的计算问题。