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

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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.