The Cuboidal Lattices and their Lattice Sums
Mathematical Physics
2021-05-20 v1 math.MP
Abstract
Lattice sums of cuboidal lattices, which connect the face-centered with the mean-centered and the body-centered cubic lattices through parameter dependent lattice vectors, are evaluated by decomposing them into two separate lattice sums related to a scaled cubic lattice and a scaled Madelung constant. Using theta functions we were able to derive fast converging series in terms of Bessel functions. Analytical continuations of these lattice sums are discussed in detail.
Keywords
Cite
@article{arxiv.2105.08922,
title = {The Cuboidal Lattices and their Lattice Sums},
author = {Antony Burrows and Shaun Cooper and Peter Schwerdtfeger},
journal= {arXiv preprint arXiv:2105.08922},
year = {2021}
}