Observables of real-time lattice dynamics in time-dependent density functional theory

I will discuss real-time simulations of lattice vibrations in solids and their signatures in spectroscopy. In particular signatures of electron-phonon coupling in optical and electron spectroscopies have long been used to investigate materials. With the increasing interest in controlling and manipulating materials properties in a non-equilibrium state, such signatures become relevant also in time-resolved measurements. I will discuss how real-time time-dependent density functional calculations can be used to understand spectral features of electron-phonon coupling of driven electronic structure in solids. A useful interpretative tool that emerges from such a treatment is the picture of a dressed electronic structure, which allows to discuss effects in driven systems without referring to perturbation theory.