The transfer of energy between electrons and ions in solids

In this review we consider those processes in condensed matter that involve the irreversible flow of energy between electrons and nuclei that follows from a system being taken out of equilibrium. We survey some of the more important experimental phenomena associated with these processes, followed by a number of theoretical techniques for studying them. The techniques considered are those that can be applied to systems containing many non-equivalent atoms. They include both perturbative approaches (Fermi's Golden Rule, and non-equilibrium Green's functions) and molecular dynamics based (the Ehrenfest approximation, surface hopping, semi-classical gaussian wavefunction methods and correlated electron-ion dynamics). These methods are described and characterised, with indications of their relative merits.