On density functional theory models for one-dimensional homogeneous materials

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.