Towards a unified ab initio description of excitations and their dynamics

The interplay between electron-electron interaction, electron-vibrational coupling, electron-hole correlation, and (potentially) spin-orbit coupling (SOC) may give rise to exciting phenomena in the response of matter to light. Many-body perturbation theory (MBPT), in particular the Bethe-Salpeter equation, is the method of choice for tackling such problems to describe what is happening in experimental probes like photoemission, optical and x-ray absorption, electron-loss spectroscopy, etc. In this talk, I will provide examples along these lines, providing in-depth analysis of the underlying processes. These examples include exciton-exciton coupling in resonant inelastic x-ray scattering (RIXS) in oxides, the structural relaxation in optically excited molecules, or the impact of vibrations and/or SOC in the optical absorption spectra of different materials. Furthermore, I will discuss first steps towards the description of time-resolved processes. All methods are implemented in the full-potential code exciting whose all-electron nature allows for treating valence and core excitations on the same footing, also fully accounting for SOC.