Density response from kinetic theory and time-dependent density-functional theory for matter under extreme conditions

The density linear response function for an inhomogeneous system of electrons in equilibrium with an array of fixed ions is considered. Two routes to its evaluation for extreme conditions (e.g., warm dense matter) are considered. The first is from a recently developed short-time kinetic equation; the second is from time-dependent density functional theory (tdDFT). The result from the latter approach agrees with that from kinetic theory in the adiabatic approximation, providing support and context for each. Both provide a connection to the phenomenological Kubo-Greenwood method for calculating transport properties. A brief proof of the van Leeuwen theorem (an essential underpinning of tdDFT) extended to the mixed states of equilibrium ensembles is given.