In this talk we will review the recent advances within density-functional and many-body based schemes to describe spectroscopic properties of complex systems with special emphasis to modeling time and spatially resolved electron spectroscopies. We will analyze the new phenomena and novel spectroscopic tools that utilize the quantum nature of light to understand and control quantum materials both in and out of equilibrium In this context we will present the theoretical approaches developed in the group (and under development) to construct a novel theoretical and computational framework that enables quantum simulations of the joint electron-ion dynamics of atomic, molecular and solids coupled to quantized electromagnetic fields opening a new avenue for the first-principle modeling of light-matter interactions. To achieve this goal, we will combine the principles of time-dependent density functional theory (TDDFT) and quantum electrodynamics (QED) into a new quantum electrodynamical-DFT approach named as “QEDFT”. This framework will allow for the characterisation of matter out of equilibrium, the control material processes at the electronic level and tailor material properties, and master energy and information on the nanoscale to propose new devices with capabilities.
