Note on crystallization for alternating particle chains

• Verfasst von: Bétermin, Laurent [VerfasserIn]
• Verfasst von: Knüpfer, Hans [VerfasserIn]
• Verfasst von: Nolte, Florian [VerfasserIn]
• Titel: Note on crystallization for alternating particle chains
• Verf.angabe: Laurent Bétermin, Hans Knüpfer, Florian Nolte
• E-Jahr: 2020
• Jahr: November 2020
• Umfang: 13 S.
• Illustrationen: Illustrationen
• Fussnoten: Online veröffentlicht am 13. Juli 2020 ; Gesehen am 10.01.2024
• Titel Quelle: Enthalten in: Journal of statistical physics
• Ort Quelle: New York, NY [u.a.] : Springer Science + Business Media B.V., 1969
• Jahr Quelle: 2020
• Band/Heft Quelle: 181(2020), 3, Seite 803-815
• ISSN Quelle: 1572-9613
• DOI: doi:10.1007/s10955-020-02603-2
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 26A51
• Sach-SW: 74E15
• Sach-SW: 82B05
• Sach-SW: Convexity
• Sach-SW: Crystallization
• Sach-SW: Energy minimization
• Sach-SW: Ionic crystals
• K10plus-PPN: 1818275309

Abstract

We investigate one-dimensional periodic chains of alternate type of particles interacting through mirror symmetric potentials. The optimality of the equidistant configuration at fixed density—also called crystallization—is shown in various settings. In particular, we prove the crystallization at any scale for neutral and non-neutral systems with inverse power laws interactions, including the three-dimensional Coulomb potential. We also show the minimality of the equidistant configuration at high density for systems involving inverse power laws and repulsion at the origin. Furthermore, we derive a necessary condition for crystallization at high density based on the positivity of the Fourier transform of the interaction potentials sum.