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

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.

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12th International Conference on Scientific Computing in Electrical Engineering (SCEE 2018), Taomina, Italy. 105–113, Springer (2020)