Density Response from Kinetic Theory and Time Dependent Density Functional Theory for Matter Under Extreme Conditions

TL;DR

This paper compares kinetic theory and time-dependent density functional theory for calculating the density response in matter under extreme conditions, validating their agreement and connecting to transport property calculations.

Contribution

It demonstrates the equivalence of kinetic theory and tdDFT approaches for extreme conditions and extends the van Leeuwen theorem to equilibrium ensembles.

Findings

Agreement between kinetic theory and tdDFT in adiabatic approximation

Connection established to Kubo-Greenwood method

Extended van Leeuwen theorem for equilibrium mixed states

Abstract

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.