Transport and optical properties of warm dense aluminum in the   two-temperature regime: Ab initio calculation and semiempirical approximation
  This work is devoted to the investigation of transport and optical properties of liquid aluminum in the two-temperature case. At first optical properties, static electrical and thermal conductivities were obtained in the \textit{ab initio} calculation. The \textit{ab initio} calculation is based on the quantum molecular dynamics, density functional theory and the Kubo-Greenwood formula. The semiempirical approximation was constructed based on the results of the \textit{ab initio} caculation. The approximation yields the dependences $\sigma_{1_\mathrm{DC}}\propto1/T_i^{0.25}$ and $K\propto T_e/T_i^{0.25}$ for the static electrical conductivity and thermal conductivity, respectively. The approximation is valid for liquid aluminum at $\rho=2.70$~g/cm$^3$, 3~kK~$\leq T_i\leq T_e\leq20$~kK. Our results are well described by the Drude model with the effective relaxation time $\tau\propto T_i^{-0.25}$. We have compared our results with a number of other models. They are all reduced in the low-temperature limit to the Drude model with different expressions for the relaxation time $\tau$. Our results are not consistent with the models in which $\tau\propto T_i^{-1}$ and support the models which use the expressions with the slower decrease of the relaxation time. 
D. V. Knyazev, P. R. Levashov
physics.plasm-ph cond-mat.mtrl-sci