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Pré-Publication, Document De Travail Année : 2018

Note on crystallization for alternating particle chains

Résumé

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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Dates et versions

hal-01761439 , version 1 (10-04-2018)
hal-01761439 , version 2 (06-03-2020)
hal-01761439 , version 3 (10-07-2020)

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Laurent Bétermin, Hans Knüpfer, Florian Nolte. Note on crystallization for alternating particle chains. 2018. ⟨hal-01761439v3⟩

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