The behavior of warm dense matter (pressures of several Mbar and temperatures of several eV) is of paramount importance for interior models of giant planets such as Jupiter and Saturn. However, the high-pressure phase diagram of even the simplest and most abundant elements hydrogen and helium as well as that of molecular systems such as water is not well known. A prerequisite for a better understanding of warm dense matter is an accurate description of the changes of the electronic properties dependent on pressure
and temperature. These changes may induce transitions from non-metallic to metallic-like conduction (H, He), demixing processes (H-He), and lead to the formation of superionic phases with proton conduction (H2O, NH3). While each of these phenomena has a strong impact on current models of the interior structure and evolution of giant planets and their magnetic fields, it also represents a major challenge to many-particle theory. We apply ab initio molecular dynamics simulations based on finite-temperature density functional theory to calculate the thermo-physical properties of warm dense matter for a wide range of densities and temperatures. For instance, a liquid-liquid phase transition is
predicted for H which is connected with the non-metal-to-metal transition. The behavior of the electrical and thermal conductivity is analyzed and deviations from the Wiedemann-Franz relation are observed. Furthermore, the parameters for demixing of He from H are
determined which match the conditions in the interior of Saturn as long has been predicted. Finally, we calculate the interior structure, composition, and cooling time of solar and extrasolar giant planets within three-layer models based on the ab initio EOS data and the conductivities.