On crystal ground state in the Schrödinger-Poisson model: point ions

Abstract

A space-periodic ground state is shown to exist for lattices of point ions in ${\mathbb{R}}^3$ coupled to the Schrödinger and scalar fields. The coupling requires the renormalization of the selfaction because of the singularity of the Coulomb potential. The ground state is constructed by minimization of the renormalized energy per cell. This energy is bounded from below when the charge of each ion is positive. The elementary cell is necessarily neutral.

10 pages. arXiv admin note: substantial text overlap with arXiv:1310.3084

References in corpus (3)

• The Hartree equation for infinitely many particles. I. Well-posedness theory
• The Hartree equation for infinitely many particles. II. Dispersion and scattering in 2D
• On crystal ground state in the Schrödinger-Poisson model

Cited by in corpus (2)

• On linear stability of crystals in the Schroedinger-Poisson model
• On the dispersion decay for crystals in the linearized Schrödinger-Poisson model