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Note on crystallization for alternating particle chains

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...

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Hauptverfasser: Bétermin, Laurent (VerfasserIn) , Knüpfer, Hans (VerfasserIn) , Nolte, Florian (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: November 2020
In: Journal of statistical physics
Year: 2020, Jahrgang: 181, Heft: 3, Pages: 803-815
ISSN:1572-9613
DOI:10.1007/s10955-020-02603-2
Online-Zugang:Verlag, kostenfrei, Volltext: https://doi.org/10.1007/s10955-020-02603-2
Verlag, kostenfrei, Volltext: https://link.springer.com/article/10.1007/s10955-020-02603-2
Volltext
Verfasserangaben:Laurent Bétermin, Hans Knüpfer, Florian Nolte

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520 |a 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. 
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