Mathematical and numerical analysis for quantum wave equations: from theory to applications

量子波动方程的数学和数值分析：从理论到应用

• 批准号: RGPIN-2018-05321
• 负责人: Lorin, Emmanuel
• 金额: $ 1.31万
• 依托单位: Carleton University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=676896
• 关键词: Mathematical; numerical; analysis; quantum; wave

This applied mathematics research program is highly motivated by strong field laser physics and Quantum ElectroDynamics (QED), which are very dynamic and fast evolving research fields in theoretical and applied physics. The latter are also the source of many current and future applications. They have even led to the birth of a new science, the celebrated Attosecond Science, dedicated to the control of electron dynamics in atoms and molecules, using ultrashort and intense laser pulses! Canada is a leader in those fields, and this research proposal intends to contribute and to strengthen their development from the mathematical and computational point of view. Indeed, the highly nonlinear and complex phenomena occurring in photonics, nonperturbative nonlinear optics, and QED require advanced and modern mathematical models and tools for their analysis, and the development of efficient and accurate computational methods for their approximation and simulation. Although the program will mainly focus on mathematical, numerical and modelling aspects, simulation codes will be also developed/improved and applications in fundamental and applied physics will be explored within interdisciplinary collaborations.

这项应用数学研究计划是由强场激光物理和量子电动力学(QED)高度推动的，这两个领域在理论和应用物理中都是非常动态和快速发展的研究领域。后者也是许多当前和未来应用的来源。他们甚至导致了一门新科学的诞生，著名的阿托秒科学，致力于控制原子和分子中的电子动力学，使用超短和强烈的激光脉冲！加拿大在这些领域处于领先地位，这项研究提案打算从数学和计算的角度促进和加强这些领域的发展。事实上，在光子学、非微扰非线性光学和量子电动力学中出现的高度非线性和复杂的现象需要先进和现代的数学模型和工具来分析它们，并开发出高效和准确的计算方法来近似和模拟它们。虽然该计划将主要集中在数学、数值和建模方面，但也将开发/改进模拟代码，并将在跨学科合作中探索基础和应用物理的应用。