Note on crystallization for alternating particle chains

Laurent Bétermin (1) , Hans Knüpfer (2) , Florian Nolte (2)

1 University of Vienna [Vienna]
2 Universität Heidelberg [Heidelberg] = Heidelberg University

We investigate one-dimensional periodic chains of alternate type of particles interacting through mirror symmetric potentials. The optimality of the equidistant configuration at any 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. Furthermore, we derive a necessary condition for crystallization at high density based on the positivity of the Fourier transform of the interaction potentials sum.

Mots clés: Crystallization; Convexity; Ionic crystals; Energy minimization

Domaines: Optimisation et contrôle [math.OC]; Physique mathématique [math-ph]

Laurent Bétermin, Hans Knüpfer, Florian Nolte. Note on crystallization for alternating particle chains. 2018. ⟨hal-01761439v2⟩