The relationship between hopping and coherent motion in dynamically disordered systems

Diverse transport processes are described within a framework previously developed only for systems undergoing random host reorganization concurrent with carrier hopping. The rule D(ω)=D₀(ω-iλ) relating frequency-dependent diffusion with and without random reorganization at rate λ is shown equivalent to a condition on the carrier velocity autocorrelation function that often applies, for physically different reasons, to both coherent and hopping transport. Formulation in terms of mean-square carrier displacement leads to rules for combining renewal (e.g. scattering and host reorganization) processes, and predicts how renewal affects frequency-dependent transport in physically different cases.