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arXiv · 1505.02365

Exciton Scattering via Algebraic Topology

Michael J. Catanzaro·Vladimir Y. Chernyak·John R. Klein
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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 well-known 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.

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BibTeXRIS

Michael J. Catanzaro, Vladimir Y. Chernyak, John R. Klein. 2015-05-10. Exciton Scattering via Algebraic Topology. https://arxiv.org/abs/1505.02365

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