Kinetic theory derivation of exchange-correlation in quantum plasma hydrodynamics

A quantum kinetic equation containing exchange-correlation described by an effective potential is derived, in a non-relativistic electrostatic quantum plasma. The velocity moments of the kinetic equation produce quantum fluid equations modified by the exchange-correlation potential. Closure of the hydrodynamic equations is achieved by expressing the pressure dyad in terms of the number density, using a quantum corrected local velocity displaced Wigner function equilibrium. The propagation of ion-acoustic waves in a quantum electron-ion plasma is analyzed, in the case of a completely degenerate electron gas. The fluid and kinetic approaches are compared and shown to agree in the long wavelength limit. A discussion on the equation of state and the role of the exchange-correlation and quantum diffraction effects is provided. Possible experimental parameters for the verification of the predictions are identified. (paper)