Dynamical fluctuations in the one particle density - comparison of different approaches

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.