From superintegrability to quasi-exact solvability: theory and application

从超可积性到准精确可解性：理论与应用

• 批准号: DP190101529
• 负责人: A/Prof Yao-Zhong Zhang
• 金额: $ 28.09万
• 依托单位: The University of Queensland
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2019
• 资助国家: 澳大利亚
• 起止时间: 2019-04-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP190101529
• 关键词: superintegrability; quasi; exact; solvability; theory

This project aims to develop mathematical techniques to resolve longstanding problems in the area of integrability and exact solvability. Quantum integrable systems and exact solvable models are of central importance for understanding the correct behaviours of complex quantum problems without approximation. This project aims to construct sophisticated mathematical tools to settle key questions across a variety of models such as superintegrable systems, quantum spin chains, and spin-boson models. Anticipated applications of the proposed research include the accurate prediction of physical phenomena, from energy spectra to quantum correlations. Such advances should have significant ramifications, and provide benefits, well beyond the mathematical discipline itself.

该项目旨在发展数学技术来解决可积性和精确可解性领域的长期问题。量子可积系统和精确可解模型对于理解复杂量子问题的正确行为至关重要，而无需近似。该项目旨在构建复杂的数学工具，以解决各种模型中的关键问题，如超可积系统，量子自旋链和自旋玻色子模型。预期的应用所提出的研究包括准确预测的物理现象，从能谱到量子关联。这样的进步应该有重大的影响，并提供远远超出数学学科本身的好处。