2018/04/16 by Laurent Bétermin, Bétermin, Laurent, Hans Knüpfer +3
Materials Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Optimization and Control (math.OC) #Quantum many-body systems #Quasicrystal Structures and Properties #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1804.05743
openalex publication_date 2018/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.