The idea to describe quantum systems within a hydrodynamic framework (quantum hydrodynamics, QHD) goes back to Madelung and Bohm. While such a description is formally exact for a single particle, more recently the concept has been applied to many-particle systems by Manfredi and Haas [Phys. Rev. B 64, 075316 (2001)] and received high popularity in parts of the quantum plasma community. Thereby, often the applicability limits of these equations are ignored, giving rise to unphysical predictions. Here we demonstrate that modified QHD equations for plasmas can be derived from Thomas-Fermi theory including gradient corrections. This puts QHD on firm grounds. At the same time this derivation yields a different prefactor, γ = (D − 2/3D), in front of the quantum (Bohm) potential which depends on the system dimensionality D. Our approach allows one to identify the limitations of QHD and to outline systematic improvements.

We study the problem of electron-ion temperature equilibration in plasmas. We consider pure H at various densities and temperatures, and Ar-doped H at temperatures high enough so that the Ar is fully ionized. Two theoretical approaches are used: classical molecular dynamics (MD) with statistical 2-body potentials, and a generalized Lenard-Balescu (GLB) theory capable of treating multi-component weakly-coupled plasmas. The GLB is used in two modes: 1) with the quantum dielectric response in the random-phase approximation (RPA) together with the pure Coulomb interaction, and 2) with the classical (h −→ 0) dielectric response (both with and without local-field corrections) together with the statistical potentials. We find that the MD results are described very well by classical GLB including the statistical potentials and without local-field corrections (RPA only); worse agreement is found when static local-field effects are included, in contradiction to the classical pure-Coulomb case with like charges. The results of the various approaches are all in excellent agreement with pure-Coulomb quantum GLB when the temperature is high enough.In addition, we show that classical calculations with statistical potentials derived from the exact quantum 2-body density matrix produce results in far better agreement with pure-Coulomb quantum GLB than classical calculations performed with older existing statistical potentials.