Optimal lattice configurations for interacting spatially extended particles

• Verfasst von: Bétermin, Laurent [VerfasserIn]
• Verfasst von: Knüpfer, Hans [VerfasserIn]
• Titel: Optimal lattice configurations for interacting spatially extended particles
• Verf.angabe: Laurent Bétermin, Hans Knüpfer
• E-Jahr: 2018
• Jahr: October 2018
• Umfang: 16 S.
• Fussnoten: Gesehen am 17.12.2018
• Titel Quelle: Enthalten in: Letters in mathematical physics
• Ort Quelle: Dordrecht [u.a.] : Springer Science + Business Media B.V, 1975
• Jahr Quelle: 2018
• Band/Heft Quelle: 108(2018), 10, Seite 2213-2228
• ISSN Quelle: 1573-0530
• DOI: doi:10.1007/s11005-018-1077-9
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Calculus of variations
• Sach-SW: Crystal
• Sach-SW: Lattice energy
• Sach-SW: Primary 74G65
• Sach-SW: Secondary 82B20
• Sach-SW: Triangular lattice
• K10plus-PPN: 1585600547

Abstract

We investigate lattice energies for radially symmetric, spatially extended particles interacting via a radial potential and arranged on the sites of a two-dimensional Bravais lattice. We show the global minimality of the triangular lattice among Bravais lattices of fixed density in two cases: In the first case, the distribution of mass is sufficiently concentrated around the lattice points, and the mass concentration depends on the density we have fixed. In the second case, both interacting potential and density of the distribution of mass are described by completely monotone functions in which case the optimality holds at any fixed density.