As a promising avenue to obtain new extreme ultraviolet light source and detect electronic properties, high-harmonic generation (HHG) has been actively developed in both theory experiment. In solids lacking inversion symmetry, when electrons undergo nonadiabatic transition, directional charge shift occurs is characterized by vector, which measures the real-space of photoexcited electron hole. F...

In many contexts, there is a need to construct C maps from a given reference domain to a family of deformed domains. In our case, the motivation comes from the application of the Arbitrary Lagrangian Eulerian (ALE) method and also the reduced basis element method. In these methods, the maps are used to construct the grid-points needed on the deformed domains, and the corresponding Jacobian of t...

We derive a Hodge decomposition of discrete vector fields on polyhedral surfaces, and apply it to the identification of vector field singularities. This novel approach allows us to easily detect and analyze singularities as critical points of corresponding potentials. Our method uses a global variational approach to independently compute two potentials whose gradient respectively co-gradient ar...

A set of gauge transformations a relativistic field quantum harmonic oscillators is studied in mathematically rigorous manner. Each wave function the domain number operator single oscillator generates Fréchet-differentiable functions. Starting from coherent one obtains two-dimensional differentiable manifold vector states. As an illustration it shown that transformation can be chosen such way r...