Harmonic Analysis and Applications

June 4-8, 2018


"Wavelets functions (WF) and time dependant Density Functional Theory (TDDFT) application to quantum abinitio models for ultra-fast femtosecond photo emission"

Babigeon, Jean-Luc

Pseudo potential formalism - corresponding roughly to softening of short range potential near atomic sites - is compatible with many complete -or not- basis solutions of the Hamiltonian. Particularly, WF basis are a demanding tool for the development of electronic wave function. They behave in a very efficient way regarding to plane wave development because of their localized character in real and reciprocal space, their orthogonality and smoothness, and finally, their adaptivity. It is a critical trend today, because even parallel simulations were recently limited to super lattices of some hundred of atoms. Until now, implementation has been shown for ground states, GS, but few advances results have evaluated their possible use for excited states computations, inside the scope of TDDFT. However, that challenging task is not trivial: for example unlike GS case, excited states are not covered by a universal Hamiltonian approach, and are in highly non equilibrium case also; doubt subsist about perturbative methods. Finally we can't consider that in spatial grid, wave functions are null ''nearly everywhere''. The present proposal is directed to 3 axes : - Review of TDDFT interfaces to WF, and elaboration of a draft theoretical model;We are to rely on recent efficient algorithms suited to the solution of non-linear partial differential equations - Implementation of model to practical codes, as BigDFT and TDDFT inside Abinit ; computation results will be shown in parallel mode, study about time computation contributions in each step of self coherent and non self coherent convergences, comparisons of convergence performances between several basis (Haar, Daubechies, Mexican...). - application to an evaluation of one photon photo emission in a special case of plane graphen. Higher interactions like photo fields or optical field emission are not considered. Our goal in particle physics, is to develop a high repetition frequency femtosecond electron source, with very low charges per bunch. This context excludes simple electrical models ; thermodynamical and quantum effects on exotic armchair emitters like graphen may be preponderant. By their plane geometry, our research presents also some analogies with the development of future nano scale electronic devices.

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