Optimal and non-optimal lattices for non-completely monotone interaction potentials
| dc.contributor.author | Betermin, Laurent | |
| dc.contributor.author | Petrache, Mircea | |
| dc.date.accessioned | 2025-01-23T21:08:59Z | |
| dc.date.available | 2025-01-23T21:08:59Z | |
| dc.date.issued | 2019 | |
| dc.description.abstract | We investigate the minimization of the energy per point Ef among d-dimensional Bravais lattices, depending on the choice of pairwise potential equal to a radially symmetric function f(|x|2). We formulate criteria for minimality and non-minimality of some lattices for Ef at fixed scale based on the sign of the inverse Laplace transform of f when f is a superposition of exponentials, beyond the class of completely monotone functions. We also construct a family of non-completely monotone functions having the triangular lattice as the unique minimizer of Ef at any scale. For Lennard-Jones type potentials, we reduce the minimization problem among all Bravais lattices to a minimization over the smaller space of unit-density lattices and we establish a link to the maximum kissing problem. New numerical evidence for the optimality of particular lattices for all the exponents are also given. We finally design one-well potentials f such that the square lattice has lower energy Ef than the triangular one. Many open questions are also presented. | |
| dc.description.funder | Mathematics Center Heidelberg (MATCH) | |
| dc.fuente.origen | WOS | |
| dc.identifier.doi | 10.1007/s13324-019-00299-6 | |
| dc.identifier.eissn | 1664-235X | |
| dc.identifier.issn | 1664-2368 | |
| dc.identifier.uri | https://doi.org/10.1007/s13324-019-00299-6 | |
| dc.identifier.uri | https://repositorio.uc.cl/handle/11534/100781 | |
| dc.identifier.wosid | WOS:000504342500027 | |
| dc.issue.numero | 4 | |
| dc.language.iso | en | |
| dc.pagina.final | 2073 | |
| dc.pagina.inicio | 2033 | |
| dc.revista | Analysis and mathematical physics | |
| dc.rights | acceso restringido | |
| dc.subject | Lattice energies | |
| dc.subject | Theta functions | |
| dc.subject | Lennard-Jones potentials | |
| dc.subject | Triangular lattice | |
| dc.subject | Completely monotone functions | |
| dc.subject | Laplace transform | |
| dc.subject | Primary 74G65 | |
| dc.subject | Secondary 82B20 | |
| dc.subject | 11F27 | |
| dc.title | Optimal and non-optimal lattices for non-completely monotone interaction potentials | |
| dc.type | artículo | |
| dc.volumen | 9 | |
| sipa.index | WOS | |
| sipa.trazabilidad | WOS;2025-01-12 |