Exciton Scattering via Algebraic Topology

Michael J. Catanzaro, Vladimir Y. Chernyak, John R. Klein

Published 2015-05-10Version 1

This mathematics paper uses algebraic and differential topology to study a significant problem in chemistry. The problem is to compute the number of electronic excitations (excitons) associated to a molecule equipped with scattering data. We will exhibit a lower bound to this number using intersection theory in the unitary group. When the segment lengths of our molecule are sufficiently large, our bound is sharp. The tools used to attack the problem are an index theorem and an explicit cell structure on the unitary group.