Time-Dependent Mixed Deterministic-Stochastic Kohn Sham Density Functional Theory for Matter in Extreme Conditions

The cubic scaling of computational costs with system size and temperature is a critical limitation for ab-initio simulations, based on Mermin density functional theory (DFT), of matter in extreme conditions. Additional real-time time-dependent DFT simulations scale linearly with the number of orbitals required to calculate the density. Our mixed-stochastic-deterministic Kohn Sham DFT algorithms can alleviate the burdon of these scaling laws. We apply this approach to the simulation of warm dense carbon system (up to 10 eV) for both electrical conductivity and electronic stopping power. We will compare calculated electronic stopping power to recent experimental measurements.