Aarhus Universitets segl

Lattice theta function and ionic crystal: a proof of Born’s conjecture

Laurent Bétermin (Villum Centre for the Mathematics of Quantum Theory, Copenhagen University)
Torsdag 27. september 2018 16:15–17:00 Aud. D3 (1531-215)
Analyseseminar

In his paper "Über elektrostatische Gitterpotentiale", published in 1921, Max Born asked the following question related to ionic crystals: "How to arrange positive and negative charges on a simple cubic lattice of finite extent so that the electrostatic energy is minimal?". He conjectured that the alternation of charges +1 and -1 is optimal distribution of charges.
In this talk, I will explain a connection between the translated lattice theta function and the optimal configuration of charges on a given lattice, when the interaction potential is completely monotone. Thus, a proof of Born’s conjecture in any dimension, for orthorhombic lattices, will be given. Finally, we will see that the solution for the triangular lattice exhibits a surprising honeycomb structure. This talk is based on joint works with Hans Knüpfer (University of Heidelberg) and Mircea Petrache (PUC Chile).
Kontakt: Søren Fournais Revideret: 31.08.2018