Hydrodynamics of superionic conductors

Using the Mori method we present a rigorous hydrodynamic theory for the collective excitations in superionic conductors at low frequencies and long wavelengths. By means of static and dynamic linear response theory all microscopic quantities of the theory are expressed as derivatives of the free energy or as transport coefficients. Explicit expressions for the dispersion and the damping of the modes and for the density correlation function are worked out for high-symmetry directions and numerically evaluated for-AgI. In particular we show that the two non-propagating modes can give rise to a small central component (width~k ², constant intensity) and a broad central component (constant width fork0, intensity ~k ²) in scattering spectra. Extrapolating our theory to larger wave vectors we offer a new explanation for the broad central component found recently in neutron scattering spectra of-AgI.