Collective Electron Dynamics in Metallic and Semiconductor nanostructures

International audienceWe review different approaches to the modeling and numerical simulation of the nonlinear electron dynamics in metallic and semiconductor nanostructures. Depending on the required degree of sophistication, such models go from the full N-body dynamics (configuration interaction), to mean-field approaches such as the time-dependent Hartree equations, down to macroscopic models based on hydrodynamic equations. The time-dependent density functional theory and the localdensity approximation - which have become immensely popular during the last two decades - can be understood as an upgrade of the Hartree approach allowing one to include, at least approximately, some effects that go beyond the mean-field. Alternative methods, based onWigner's phase-space representation of quantum mechanics, are also described. Wigner's approach has the advantage of permitting a more straightforward comparison between semiclassical and fully quantum results. As an illustrative example, the many-electron dynamics in a semiconductor quantum well is studied numerically, using both a mean-field approach (Wigner-Poisson system) and a quantum hydrodynamical model. Finally, the above methods are extended to include the spin degrees of freedom of the electrons. The local-spin-density approximation is used to investigate the linear electron response in metallic nanostructures. The modeling of nonlinear spin effects is sketched within the framework of Wigner's phase-space dynamics