Authors: Winfried Lorenzen, Martin French, Bastian Holst, Ulrike Kramm, Nadine Nettelmann, Ronald Redmer

We have calculated an accurate ab initio EOS for hydrogen, helium, and water by using quantum molecular dynamics simulations. This data is used for modelling Giant Planets like Jupiter, Saturn, and also for some extrasolar planets. The planetary models reproduce all observational constraints and yield mass-radius relations for extrasolar planets. An important phenomenon for giant planets and their evolution is the demixing of hydrogen and helium at high pressures. By using the ab initio EOS for hydrogen-helium mixtures we have derived the region of demixing. The results can explain the lower helium fraction in Jupiter's and Saturn's atmosphere compared to the protosolar value and the high luminosity of Saturn.