My research is presently divided into three parts.

i) Optical spectroscopy of individual nanostructures such as quantum wires and quantum dots

I am mostly interested in the electronic structure of crystal phase heterostructures. Such interfaces are perfectly flat and have no atomic intermixing either. They are thus much more interesting than conventional heterostructures involving different materials. I prefer when a separate technique such as photoluminescence and resonant Raman scattering is performed on the same sample. Experiments are always compared with realistic calculations.

ii) Realistic calculations of the properties of semiconductor nanostructures

This involves realistic k.p-calculation in full 3D. This project is in collaboration with Prof. Craig Pryor, University of Iowa. We cannot only calculate the gross band-structure, we can also compute the detailed many-body states including up to six particles.

iii) Development of new techniques in manybody theory using functional analysis and deep learning

This project concerns the characterization of the set of pair densities that can arise from a wavefunction. Let us call this set P(N), where N is the number of particles considered. It is unknown how to recognize if a function belongs to P(N) but I have found that neural networks can do this fairly easily. I have also applied deep learning to other problems in theoretical physics and mathematics.