Isochoric, isobaric and ultrafast conductivities of aluminum, lithium and carbon in the warm dense matter (WDM) regime

We study the conductivities $\sigma$ of (i) the equilibrium isochoric state (${\sigma }_{\mathrm{i}\mathrm{s}}$), (ii) the equilibrium isobaric state (${\sigma }_{\mathrm{i}\mathrm{b}}$), and also the (iii) non-equilibrium ultrafast matter (UFM) state ($\sigma_{\rm uf}$)withtheiontemperature$T_i$lessthanthetheelectrontemperature$T_e$. Aluminum, lithium and carbon are considered, being increasingly complex warm dense matter (WDM) systems, with carbon having transient covalent bonds. First-principles calculations, i.e., neutral-pseudoatom (NPA) calculations and density-functional theory (DFT) with molecular-dynamics (MD) simulations, are compared where possible with experimental data to characterize $\sigma_{\rm ic}, \sigma_{\rm ib}$and$\sigma_{\rm uf}$\mathrm{.}TheNPA$\sigma_{\rm ib}$ are closest to the available experimental data when compared to results from DFT+MD, where simulations of about 64-125 atoms are typically used. The published conductivities for Li are reviewed and the value at a temperature of 4.5 eV is examined using supporting X-ray Thomson scattering calculations. A physical picture of the variations of $\sigma$ with temperature and density applicable to these materials is given. The insensitivity of $\sigma$ to $T_e$ below 10 eV for carbon, compared to Al and Li, is clarified.