Ion dynamics and energy relaxation rate in nonequilibrium electron-ion systems

We rigorously derive an analytical expression for the energy equilibration rate in nonequilibrium electron-ion systems that is valid for a large class of systems including solid and liquid metals, warm dense matter, and hot, weakly coupled plasmas. To this end we first derive a generalized Langevin equation that describes the motion of the classical ions in the quantum mechanical environment of the electrons. A general expression for the energy relaxation rate is then obtained assuming that each subsystem is in thermal equilibrium with itself. Direct approximations naturally reproduce the popular results of Landau and Spitzer for hot plasmas and the Fermi golden rule result for dense matter. We propose a method to evaluate numerically the energy relaxation rate with finite-temperature density functional theory calculations in difficult regimes such as the warm dense matter regime where neither quantum nor strong coupling effects can be ignored.