Crystallization of one-dimensional alternating two-component systems

Abstract : We investigate one-dimensional periodic chains of alternate type of particles interacting through mirror symmetric potentials. The optimality of the equidistant configuration – also called crystallization – is shown in various settings, at any scale and at high density. 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 prove the crystallization at high density for Lennard-Jones type interactions and ionic screened potentials involving inverse power laws and Yukawa potentials. These high density results are derived from a general sufficient condition based on a convexity argument. 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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Contributor : Laurent Bétermin <>
Submitted on : Tuesday, April 10, 2018 - 5:15:48 PM
Last modification on : Wednesday, June 12, 2019 - 3:30:03 PM


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  • HAL Id : hal-01761439, version 1
  • ARXIV : 1804.05743



Laurent Bétermin, Hans Knüpfer, Florian Nolte. Crystallization of one-dimensional alternating two-component systems. 2018. ⟨hal-01761439⟩



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