Minimization of energy per particle among Bravais lattices in ℝ2: Lennard–Jones and Thomas

Minimization of energy per particle among Bravais lattices in ℝ2: Lennard–Jones and Thomas–Fermi cases

Published:2015-10-29 Issue:06 Volume:17 Page:1450049
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

Bétermin Laurent¹,Zhang Peng¹

Affiliation:

1. Université Paris-Est Créteil, LAMA – CNRS UMR 8050, 61, Avenue du Général de Gaulle, 94010 Créteil, France

Abstract

We prove in this paper that the minimizer of Lennard–Jones energy per particle among Bravais lattices is a triangular lattice, i.e. composed of equilateral triangles, in ℝ2 for large density of points, while it is false for sufficiently small density. We show some characterization results for the global minimizer of this energy and finally we also prove that the minimizer of the Thomas–Fermi energy per particle in ℝ2 among Bravais lattices with fixed density is triangular.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199714500497

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