Dense quantum plasmas - failures of quantum hydrodynamic models

Dense quantum plasmas have been successfully described in recent decades using a variety of methods such as quantum statistics, quantum kinetic theory and first principle simulations [1]. The high theoretical effort has stimulated attempts for a simplified description where a particular popularity has received quantum hydrodynamics (QHD) [2]. However, very often the limitations of QHD are ignored, giving rise to numerous predictions that are in contrast to basic quantum many-body theory. A recent striking example are the predictions of an attractive proton-proton potential in dense hydrogen and [3]. We will discuss the reason for this failure of QHD [4] and draw conclusions for the applicability of this approach.\\[4pt] [1] M. Bonitz, ``Quantum Kinetic Theory,'' Teubner, Stuttgart, Leipzig 1998\\[0pt] [2] G. Manfredi, and F. Haas, Phys. Rev. B {\bf 64}, 075316 (2001).\\[0pt] [3] P.K. Shukla, and B. Eliasson, Phys. Rev. Lett. {\bf 108}, 165007(2012).\\[0pt] [4] M. Bonitz, E. Pehlke, and T. Schoof, Phys. Rev. E {\bf 87}, 033105 (2013).