### Warm Dense Matter

(Figure by Mike Desjarlais)

Warm dense matter (WDM) is encountered in systems as diverse as the interiors of giant planets and in the pathway to inertial confinement fusion. WDM is challenging to theory and simulation because it occurs inconveniently, for theory, between the comparatively well-studied plasma and condensed matter regimes. Both the Coulomb coupling parameter $$\Gamma := Q^2/(r_s k_B {\rm T})$$ and electron degeneracy parameter $$\Theta := k_B {\rm T}/\epsilon_F$$ are approximately unity for WDM. ($$Q =$$ relevant charge, $$r_s =$$ Wigner radius, $$\epsilon_F =$$ electron Fermi energy, $${\rm T} =$$ temperature, $$k_B =$$ Boltzmann constant.) A non-perturbative treatment therefore is required.

Contemporary computations on WDM are dominated by use of the Kohn-Sham realization of thermal density functional theory (DFT) to generate a potential surface for ionic motion (treated classically). The great majority of these calculations use approximate ground-state exchange-correlation functionals, $$E_{xc}$$, with the XC temperature-dependence picked up implicitly from the $$\rm T$$-dependence of the density $$n({\mathbf r},{\rm T})$$. Though fruitful, this approach is not without potential difficulties.

OFDFT