On a Bloch-type model with electron-phonon interactions: modeling and numerical simulations

Abstract

In this work, we discuss how to take into account electron-phonon interactions in a Bloch type model for the description of quantum dots. The model consists in coupling an equation on the density matrix with a set of equations on quantities called phonon-assisted densities, one for each phonon mode. After a description of the model, we discuss how to discretize efficiently this non-linear coupling in view of numerical simulations.