Counting the number of excited states in organic semiconductor systems   using topology
  Exciton Scattering (ES) theory attributes excited electronic states to standing waves in quasi-one-dimensional molecular materials by assuming a quasi-particle picture of optical excitations. The quasi-particle properties at branching centers are described by the corresponding scattering matrices. Here we identify the topological invariant of scattering center, referred to as its winding number, and apply topological intersection theory to count the number of quantum states in a quasi-one-dimensional system. 
Michael J. Catanzaro, Tian Shi, Sergei Tretiak, Vladimir Y. Chernyak
physics.chem-ph math-ph math.AT math.MP