Dynamic conductivity of superionic conductors in an interacting Brownian particle model

The mobile ion dynamics in superionic conductors is described by a many-particle Fokker-Planck equation. A time-dependent mean-field equation for the single-particle distribution is derived, which implies a general relationship between the dynamic conductivity and structural properties. We find that the low-frequency diffusive regime is governed by a renormalized single-particle potential, whereas the high-frequency vibrational response is determined by the bare interaction between the two species of conducting and lattice ions. Numerical results, based on matrix continued fractions are presented for the whole frequency-range and implications with respect to experiments are discussed.