Multidomain Multiscale Simulation of the Coupled Maxwell-Schroedinger Equations

为了描述强电磁脉冲与物质的相互作用，人们必须使用具有原子级电荷和电流的微观麦克斯韦方程，该方程是通过求解薛定谔方程得到的。电子动力学受电磁场的影响，反之亦然，需要通过耦合麦克斯韦方程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埃量级的原子半径和键长决定。这个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在平等的基础上描述电子-离子动力学和电磁波在物质中的传播。这一方法有望在统一的麦克斯韦量子框架下研究材料的电子、磁性、光学和结构性质。除了在描述电磁场和物质相互作用的含时第一原理量子力学模拟中探索新的前沿之外，这个项目的更广泛影响涉及培养学生和博士后，他们将有一个独特的机会来学习和展示创造力，进行高调的科学研究。该项目还将涉及广泛的外联和教育活动，包括通过范德比尔特教师研究体验计划接待高中教师，通过参加范德比尔特暑期学院教育中学生，通过纳米科学演示和在纳什维尔探险科学中心的讲座让儿童参与社区。

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.