A Fourier Integral Formula for Logarithmic Energy

Frerick, L.; Müller, J.; Thomaser, T.

doi:10.1007/s11118-024-10125-9

Potential Anal

2024

DOI: 10.1007/s11118-024-10125-9

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A Fourier Integral Formula for Logarithmic Energy

L. Frerick,

J. Müller,

T. Thomaser

Abstract: A formula which expresses logarithmic energy of Borel measures on $$\mathbb {R}^n$$ R n in terms of the Fourier transforms of the measures is established and some applications are given. In addition, using similar techniques a (known) formula for Riesz energy is reinvented.

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On density functional theory models for one-dimensional homogeneous materials

Bensiali,

Lahbabi,

Maichine

et al. 2024

Journal of Mathematical Physics

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This paper studies Density Functional Theory (DFT) models for homogeneous 1D materials in the 3D space. It follows the previous work [Gontier et al., Commun. Math. Phys. 388, 1475–1505 (2021)] about DFT models for homogeneous 2D materials in 3D. We show how to reduce the problem from a 3D energy functional to a 2D energy functional. The kinetic energy is treated as in the 2D material case by diagonalizing admissible states, and writing the kinetic energy as the infimum of a modified kinetic energy functional on reduced states. Besides, we treat here the Hartree interaction term in 2D, and show how to properly define the mean-field potential, through Riesz potential. We then show the well-posedness of the reduced model and present some numerical illustrations.

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On density functional theory models for one-dimensional homogeneous materials

Bensiali,

Lahbabi,

Maichine

et al. 2024

Journal of Mathematical Physics

View full text Add to dashboard Cite

show abstract

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A Fourier Integral Formula for Logarithmic Energy

Abstract: A formula which expresses logarithmic energy of Borel measures on $$\mathbb {R}^n$$ R n in terms of the Fourier transforms of the measures is established and some applications are given. In addition, using similar techniques a (known) formula for Riesz energy is reinvented.

Cited by 1 publication

References 18 publications

On density functional theory models for one-dimensional homogeneous materials

On density functional theory models for one-dimensional homogeneous materials

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