Professor Vladimir Chernyak, from Wayne State University of USA is going to give a talk . Please attend on time if you are interested in.

Below is the talk information:

Time: 10:00 am, Oct 4th, 2013, Beijing Time

Place: A306, West Bldg 1, Qujiang Campus

Title: Topological Properties of Scattering Matrices on Graphs: Counting the Number of Standing Waves in Quasi-One-Dimensional Systems

Abstract:

Exciton scattering (ES) theory attributes excited electronic states in quasi-one-dimensional molecular materials to standing waves, 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 a 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.

The approach is based on representing the problem of solving the ES equations to an intersection problem, followed by computation of the corresponding intersection index, the latter counting intersections weighted with 1 sign factors. Therefore, the intersection index, which, being a topological (homotopy) invariant, can be easily computed, provides a lower bound for the number of ex-citations in a branched structure, represented by a weighted graph. We further demonstrate, using quantum-mechanical perturbation theory, that, when the linear segments in a branching structure are long enough, the aforementioned bound becomes tight, i.e., the intersection index actually counts the number of electronic excitations.