Static and dynamic conductivity of warm dense matter within a density-functional approach: Application to aluminum and gold

The conductivity $\sigma \left(\omega \right)$ of dense Al and Au plasmas is considered where all the needed inputs are obtained from density-functional theory (DFT). These calculations involve a self-consistent determination of (i) the equation of state and the ionization balance, (ii) evaluation of the ion-ion and ion-electron pair-distribution functions, (iii) determination of the scattering amplitudes, and finally the conductivity. We present results for Al and Au for compressions 0.1–2.0, and in the temperature range $T=0.1–10\mathrm{eV}$. Excellent agreement with recent first-principles calculations using multi-ion density-functional molecular dynamics is obtained where the data fields overlap. We review first-principles approaches to the optical conductivity, including many-body perturbation theory, molecular-dynamics evaluations, and simplified time-dependent DFT. The modification to the Drude conductivity in the presence of shallow bound states in typical Al plasmas is examined and numerical results are given at the level of the Fermi Golden Rule and an approximate time-dependent DFT.