  The metallic regime of the hydrogen plasma is studied by ab initio Molecular
Dynamics simulations, for classical protons and fully degenerate electrons, in
the strong coupling regime of the protons. The breakdown of linear screening
observed for decreasing density gives rise to a surprisingly rich
low-temperature phase diagram, showing in particular a dramatic drop of the
melting temperature of the proton crystal. Extensive dynamical simulations
reveal the remarkable persistence of a weakly damped high-frequency ion
acoustic mode (plasmon-like), even under conditions of strong electron
screening. This collective mode should disappear in the molecular phase, thus
providing a probe for the metal-insulator transition in a region of parameters
where experiment is difficult to achieve. Finite-size effects arising in the
simulation of liquid metals are discussed. The status of the dense Hydrogen
matter is extensively reviewed in the introduction.
