Swift nuclei moving through condensed matter and slowing down by electronic friction give rise to a paradigmatic problem of quantum dissipation at the nanoscale that is both strongly out of equilibrium and non adiabatic (at its least adiabatic, tens to thousands of eV transferred per Angstrom). In addition to its clear fundamental importance, the relevance of the problem to medicine and to the nuclear and aerospace industries has given rise to a century of intense research [1]. Understanding and modelling were, however, limited to building on two key frameworks: Lindhard's linear response [1], valid for any material but assuming weak perturbation, and the homogeneous electron liquid, allowing for strong perturbation but for an idealised metal [1,2], which led to very qualitative understanding of experimental results outside those regimes.

Recently, however, there has been significant progress on several relevant fronts. On one hand, a line of direct first-principles simulation of those processes started in 2007 (for a review see [3]), based on real-time time-dependent density-functional theory (RT-TDDFT), following the electron dynamics when a nucleus moves across a simulation box.  In spite of several fundamental approximations (classical nuclei, adiabatic exchange-correlation), the technique has proven quite successful in a variety of materials [3-6], and is offering new insights into the general problem.

Simultaneously, there has been progress in the theoretical underpinnings, from very general results for the low velocity regime for any metal [7], to a Floquet formalism for any periodic solid [8]. The former is based on density-functional theory, and current-density-functional theory (TDCDFT), exploring the non-locality in space and time (in the linear-response limit for low velocity), which opens the possibility of incorporating TDCDFT into simulations, and possibly extend them beyond metals. The latter, together with Floquet-TDDFT [9] (possibly extended to Floquet-TDCDFT), should allow for accurate but accessible dissipation calculations in periodic solids beyond what achieved so far.

The Ehrenfest coupled dynamics of quantum electrons and classical nuclei has its pitfalls and limitations (such as lack of thermalization), so far hard to overcome in realistic simulations. Recent developments in the coupled quantum dynamics of electrons and nuclei has proven successful in other contexts [10-15], and should allow for progress in this context as well. The added challenge in this context is the electronic continuum, as opposed to the discrete potential energy surfaces on which most progress on non-adiabatic dynamics has been achieved (e.g. in Chemistry, see [20]). Actually, both in the coupled quantum electron-nuclei dynamics and in the TDDFT contexts, the main topic of this workshop should represent an important opportunity and challenge.

Finally, one of the reasons for the slow pace of advance in this topic is the great difficulty in experiments, but which have also progressed in recent times, in the measurement of energy loss [16,17], of optical response (see e.g. opacity measurements in irradiated insulators [18]) and for ions bouncing off or reacting on metallic surfaces [19]. The workshop should allow new synergies theory-simulation-experiments, including the identification of most suitable target systems to confront jointly towards  advancing the field.