Fluctuating quantum kinetic theory

We consider a quantum Langevin kinetic equation for system of fermions. first derive the force noise correlation functions in Landau's Fermi-liquid theory from general considerations. then use resulting to calculate equilibrium dynamic structure factor collisionless regime at low temperatures. The result is agreement with conventional many-body result. both fluctuating Navier-Stokes equations fluid and hydrodynamic fermions presence quenched disorder. also discuss modifications needed describe an electron long-ranged interactions, we prove $H$ theorem nonlinear Landau equation.