Multidomain Multiscale Simulation of the Coupled Maxwell-Schroedinger Equations

耦合麦克斯韦-薛定谔方程的多域多尺度仿真

• 批准号: 1314463
• 负责人: Kalman Varga
• 金额: $ 30万
• 依托单位: Vanderbilt University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-08-01 至 2017-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1314463&HistoricalAwards=false
• 关键词: Multidomain; Multiscale; Simulation; Coupled; Maxwell

To describe the interaction of a strong electromagnetic pulse and matter, one has to use the microscopic Maxwell equations with atomic level charges and currents obtained by solving the Schroedinger equation. The electron dynamics is influenced by the electromagnetic fields and vice versa, requiring a unified treatment of electrons and the electromagnetic fields by coupling the Maxwell and Schroedinger equations. Solving this on the computer is an outstanding problem because the simulation is inherently multiscale in nature, with the spatial scale of the electromagnetic field being determined by laser wavelengths of the order of one micron and the spatial scale of electron dynamics being set by the atomic radius and bond length of the order of an Angstrom. The main objective of this project is to develop a time-dependent simulation framework to describe the electron-ion dynamics and the propagation of electromagnetic waves in matter on equal footing using a time-dependent multidomain decomposition method. This approach is expected to allow the study of electronic, magnetic, optical and structural properties of materials in a unified Maxwell-quantum framework.In addition to exploring new frontiers in simulations of time-dependent first-principles quantum mechanics to describe the interaction of electromagnetic fields and matter, the broader impacts of this project involve the training of a student and postdoc, who will have a unique opportunity to learn and demonstrate creativity in performing high-profile scientific research. This project will also involve a broad range of outreach and educational activities that include hosting high school teachers through the Vanderbilt Research Experiences for Teachers program, educating middle school students through participation in the Vanderbilt Summer Academy, engaging children in the community through nanoscience demonstrations and talks at the Nashville Adventure Science Center.

为了描述强电磁脉冲与物质的相互作用，必须使用微观麦克斯韦方程，通过求解薛定谔方程获得原子级电荷和电流。电子动力学受到电磁场的影响，反之亦然，需要通过耦合麦克斯韦和薛定谔方程来统一处理电子和电磁场。在计算机上解决这个问题是一个突出的问题，因为模拟本质上是多尺度的，电磁场的空间尺度由一微米量级的激光波长决定，电子动力学的空间尺度由原子半径决定和键长为埃量级。该项目的主要目标是开发一个与时间相关的模拟框架，使用与时间相关的多域分解方法来平等地描述物质中的电子-离子动力学和电磁波的传播。这种方法有望允许在统一的麦克斯韦量子框架中研究材料的电子、磁、光学和结构特性。除了探索与时间相关的第一原理量子力学模拟的新前沿，以描述电磁相互作用领域和问题，该项目更广泛的影响涉及对学生和博士后的培训，他们将有独特的机会学习和展示在进行备受瞩目的科学研究中的创造力。该项目还将涉及广泛的外展和教育活动，包括通过范德比尔特教师研究经验计划接待高中教师，通过参加范德比尔特暑期学院对中学生进行教育，通过纳米科学演示和讲座吸引社区儿童参与在纳什维尔探险科学中心。