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arXiv · 1909.00593

A theoretical investigation of time-dependent Kohn-Sham equations: new proofs

Gabriele Ciaramella·Martin Sprengel·Alfio Borzi
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Abstract

In this paper, a new analysis for existence, uniqueness, and regularity of solutions to a time-dependent Kohn-Sham equation is presented. The Kohn-Sham equation is a nonlinear integral Schroedinger equation that is of great importance in many applications in physics and computational chemistry. To deal with the time-dependent, nonlinear and non-local potentials of the Kohn-Sham equation, the analysis presented in this manuscript makes use of energy estimates, fixed-point arguments, regularization techniques, and direct estimates of the non-local potential terms. The assumptions considered for the time-dependent and nonlinear potentials make the obtained theoretical results suitable to be used also in an optimal control framework.

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Gabriele Ciaramella, Martin Sprengel, Alfio Borzi. 2019-09-02. A theoretical investigation of time-dependent Kohn-Sham equations: new proofs. https://arxiv.org/abs/1909.00593

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