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arXiv · 1701.02679

Investigation of optimal control problems governed by a time-dependent Kohn-Sham model

Martin Sprengel·Gabriele Ciaramella·Alfio Borzì
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Abstract

Many application models in quantum physics and chemistry require to control multi-electron systems to achieve a desired target configuration. This challenging task appears possible in the framework of time-dependent density functional theory (TDDFT) that allows to describe these systems while avoiding the high dimensionality resulting from the multi-particle Schrödinger equation. For this purpose, the theory and numerical solution of optimal control problems governed by a Kohn-Sham TDDFT model are investigated, considering different objectives and a bilinear control mechanism. Existence of optimal control solutions and their characterization as solutions to Kohn-Sham TDDFT optimality systems are discussed. To validate this control framework, a time-splitting discretization of the optimality systems and a nonlinear conjugate gradient scheme are implemented. Results of numerical experiments demonstrate the computational capability of the proposed control approach.

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Martin Sprengel, Gabriele Ciaramella, Alfio Borzì. 2017-01-10. Investigation of optimal control problems governed by a time-dependent Kohn-Sham model. https://doi.org/10.1007/s10883-017-9393-4

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