Mathematical models, methods and numerical approximations for quantum non-relativistic and relativistic mechanics and electrodynamics with application to nonlinear optics

该计划涉及量子非相对论和相对论力学中新的数学模型，方法和数值近似的发展，并应用于非线性光学。当短而强的激光脉冲在气体中传播时，其动机是为物理界提供精确和严格推导的数学模型，以及现实的模拟，以理解和优化新观察到的现象。这项研究可能对物理学和工程学的几个热门话题有用，例如：阿秒科学（利用短而强的激光脉冲控制分子内动力学），丝化（激光脉冲能够在没有引导机制的情况下传播很远的距离），量子成像，激光聚变（与控制核聚变产生能量有关）和粒子-反粒子对的产生。

This program deals with the development of new mathematical models, methods and numerical approximations in quantum non-relativistic and relativistic mechanics, with applications to nonlinear optics. The motivation is to provide to the physics community accurate and rigorously derived mathematical models, as well as realistic simulations to understand and to optimize newly observed phenomena, when short and intense laser pulses propagate in a gas. Potentially, this research could useful in several hot topics in physics and engineering, such as: attosecond science (control of the intra-molecular dynamics using short and intense laser pulses), filamentation (laser pulses having the ability to propagate over very large distances without guiding mechanism), quantum imaging, laser-fusion (with relation to controlled nuclear fusion for energy production) and particle-antiparticle pair production.