Classical mappings for electronic states

The flow of electronic excitations through matter is central to many scientific problems, from photosynthesis and the development of new solar technologies, to molecular scale electronics and the next generation of computing devices. As these technologies move toward the nanoscale, the interplay between the motion of electrons and the motion of the atomic nuclei becomes very important.

Full quantum dynamics with atomistic resolution will not be feasible, so we develop semiclassical approaches instead. One of the tricks we use is to convert the electronic quantum dynamics into classical dynamics. This approach was originally developed by Meyer and Miller, and was later shown by Stock and Thoss to be exact under certain circumstances, and has been very successful in describing nonadiabatic dynamics where there’s only one exciton. But with multiple excitons, the fermionic behavior can become important.

I developed a variant of this classical mapping approach which could be used for systems like molecular electronics, where there are many excitons and their fermionic character is important. We found that these methods were quite efficient and accurate, although I moved on to other topics after my Ph.D.