Nonlinear quantum fluid equations for a finite temperature Fermi plasma

Nonlinear quantum electron fluid equations are derived, taking into account the moments of the Wigner equation and by using the Fermi–Dirac equilibrium distribution for electrons with an arbitrary temperature. A simplified formalism with the assumptions of incompressibility of the distribution function is used to close the moments in velocity space. The nonlinear quantum diffraction effects into the fluid equations are incorporated. In the high-temperature limit, we retain the nonlinear fluid equations for a dense hot plasma and in the low-temperature limit, we retain the correct fluid equations for a fully degenerate plasma.