  Diffusion coefficients are obtained from linear response functions and from
the quantal fluctuation dissipation theorem. They are compared with the results
of both the theory of hydrodynamic fluctuations by Landau and Lifschitz as well
as the Boltzmann-Langevin theory. Sum rules related to conservation laws for
total particle number, momentum and energy are demonstrated to hold true for
fluctuations and diffusion coefficients in the quantum case.
