Mathematical Models for Transport in Macroscopic and Mesoscopic Systems - Abstract

Goudon, Thierry

Asymptotics problems for Laser-matter modeling; quantum and classical models

This joint work with F. Castella and P. Degond is devoted to the asymptotic analysis of both quantum and classical models which are intended to describe the evolution of electrons subject to the potential of an atomic crystal perturbed by the highly oscillating potential of external electro-magnetic waves. The problem combines homogenization aspects of transport like equation with relaxation phenomena. We derive either Einstein rate equations or diffusion equations with respect to the energy variable, depending on whether the initial model is quantum or classical. We point out the analogies and differences in the treatment of the two models, considering successively the cases of (quasi-)periodic perturbations or random ones. We point out the different role of the relaxation effects according to the nature of the perturbation.