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Note on crystallization for alternating particle chains

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.
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https://hal-upec-upem.archives-ouvertes.fr/hal-01761439
Contributor : Laurent Bétermin <>
Submitted on : Friday, July 10, 2020 - 9:15:54 AM
Last modification on : Friday, July 10, 2020 - 4:20:08 PM

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  • HAL Id : hal-01761439, version 3
  • ARXIV : 1804.05743

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

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