Frequency-dependent conductivity of ions in blocked linear channels

We analyze the dielectric response of mobile potassium ions within the one-dimensional channels of hollandite (${\mathrm{K}}_{2x}{\mathrm{Mg}}_x{\mathrm{Ti}}_{8-x}{\mathrm{O}}_{16}$, $x\sim 0.77$) which has been doped with small amounts (0.5-3.3 at.%) of cesium. At low temperatures the potassium ions show an anomalous diffusion confined to the segments between the Cs ions; at higher temperatures the Cs ions show their own, slow mobility. The data are quantitatively interpreted in terms of a "moving-box" model.