Towards \textit{ab initio}simulation of warm dense matter

Warm dense matter (WDM) -- an exotic state where electrons are quantum degenerate and ions may be strongly correlated -- is ubiquitous in astrophysics and highly compressed laboratory plasmas. We have recently obtained \textit{ab initio}thermodynamic results for the electron component in WDM based on novel quantum Monte Carlo (QMC) simulations [1-3] including the first \textit{ab initio}parametrization of the exchange-correlation free energy F\textunderscore xc [3, 4], and here we present applications using finite temperature DFT simulations. In addition, also inhomogeneous systems have been studied giving rise to \textit{ab initio}results for the static structure factor. Moreover, recently the first exact QMC result for the dynamic structure factor could be obtained [5]. An interesting result is the prediction of a negative plasmon dispersion in the range of strong electronic correlations -- an effect that should be observable in dense hydrogen. Finally, an outlook is presented on how to accurately treat degenerate electrons in WDM out of equilibrium. Here we discuss two approaches: quantum hydrodynamics for which a microscopic derivation is given [6]. The second is nonequilibrium Green functions which allow for a rigorous extension of kinetic equations to ultrafast relaxation processes [7]. [1] T. Schoof, S. Groth, J. Vorberger, and M. Bonitz, Phys. Rev. Lett. , 130402 (2015) [2] T. Dornheim, S. Groth, T. Sjostrom, F.D. Malone, W.M.C. Foulkes, and M. Bonitz, \underline {Phys. Rev. Lett. , 156403 (2016)} [3]S. Groth, T. Dornheim, T. Sjostrom, F.D. Malone, W.M.C. Foulkes, and M. Bonitz, \underline {Phys. Rev. Lett. , 135001 (2017)} [4] T. Dornheim, S. Groth, and M. Bonitz, Phys. Reports , 1-86 (2018) [5] T. Dornheim, S. Groth, J. Vorberger, and M. Bonitz, Phys. Rev. Lett. , 255001 (2018) [6] M. Bonitz, Zh. Moldabekov, and T. Ramazanov, Phys. Plasmas, submitted [7] M. Bonitz, ``Quantum Kinetic Theory'', 2$^{\mathrm{nd}}$ed., Springer 2016