Minimization of the discrete interaction energy with smooth potentials

Abstract

We study the pair interaction on flat tori of functions whose Fourier coefficients are positive and decay sufficiently rapidly. In dimension one we find that the minimizer, up to translation, is the equidistant point set. In dimension two, minimizing with respect to triplets we find that the minimizer is the triangular lattice.

0

Turn this paper into a full lesson

ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.

Discussion (0)

Sign in to join the discussion.

Loading comments…