van Leeuwen Theorem for Mixed States and Finite Temperature Density Response

A simple proof of the van Leeuwen theorem for existence and uniqueness of v-representability in finite-temperature time-dependent density functional theory is described. It is used to construct the linear density response function for a system of electrons in a random configuration of ions, in terms of its corresponding non-interacting form. The relevance of this for justifying the Kubo-Greenwood model for transport properties in warm, dense matter, and its context, is described. The density response function in the "adiabatic approximation" is shown to be the same as that from a recent exact short time kinetic theory [1]. This provides a further characterization of that approximation, and makes connection to the many-body methods of kinetic theory. 1. On the Kubo-Greenwood Model for Electron Conductivity, J. Dufty, J. Wrighton, K. Luo, and S. Trickey, submitted to Contr. Plasma Phys., arXiv:1709.04732.