Exciton Scattering via Algebraic Topology
Abstract
This paper introduces an intersection theory problem for maps into a smooth manifold equipped with a stratification. We investigate the problem in the special case when the target is the unitary group and the domain is a circle. The first main result is an index theorem that equates a global intersection index with a finite sum of locally defined intersection indices. The local indices are integers arising from the geometry of the stratification. The result is used to study a wellknown problem in chemical physics, namely, the problem of enumerating the electronic excitations (excitons) of a molecule equipped with scattering data. We provide a lower bound for this number. The bound is shown to be sharp in a limiting case.
 Publication:

arXiv eprints
 Pub Date:
 May 2015
 arXiv:
 arXiv:1505.02365
 Bibcode:
 2015arXiv150502365C
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematical Physics;
 Mathematics  Geometric Topology;
 92E10;
 57R19 (Primary);
 57N80;
 81V55 (Secondary)
 EPrint:
 Final version