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

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2021

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Sprengel, Martin
Borzì, Alfio

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https://doi.org/10.1080/00036811.2019.1679792
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Applicable Analysis. Taylor & Francis. 2021, 100(10), pp. 2254-2273. ISSN 0003-6811. eISSN 1563-504X. Available under: doi: 10.1080/00036811.2019.1679792

Zusammenfassung

In this paper, a new analysis for the existence, uniqueness, and regularity of solutions to a time-dependent Kohn–Sham equation is presented. The Kohn–Sham equation is a nonlinear integral Schrödinger 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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Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Kohn–Sham model, time-dependent density functional theory, nonlinear Schrödinger equation

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ISO 690CIARAMELLA, Gabriele, Martin SPRENGEL, Alfio BORZÌ, 2021. A theoretical investigation of time-dependent Kohn–Sham equations : new proofs. In: Applicable Analysis. Taylor & Francis. 2021, 100(10), pp. 2254-2273. ISSN 0003-6811. eISSN 1563-504X. Available under: doi: 10.1080/00036811.2019.1679792
BibTex
@article{Ciaramella2021theor-48645,
  year={2021},
  doi={10.1080/00036811.2019.1679792},
  title={A theoretical investigation of time-dependent Kohn–Sham equations : new proofs},
  number={10},
  volume={100},
  issn={0003-6811},
  journal={Applicable Analysis},
  pages={2254--2273},
  author={Ciaramella, Gabriele and Sprengel, Martin and Borzì, Alfio}
}
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