A key factor for the efficiency in nanostructured devices is the charge transport. Despite considerable attention to this subject, the precise nature of transport processes in these systems has remained unresolved. To understand the microscopic aspects of carrier dynamics, we suggest a method for the calculation of correlation functions. They can be expressed as the Fourier transform of a kernel containing the frequency-dependent conductivity (). We present results for the velocity correlation functions <v(o)v(t)>, the mean square deviation of position R2=<[R(t)-R(o)]2> and the diffusion coefficient D=(R2/t) in materials, like TiO2, ZnO, Si, for which a Drude-Lorentz description or its generalizations applies with a good agreement with experiments. We find that D=0, indicating absence of diffusion at long times, except in the Drude case (o=0). For small times t/<1, however, diffusion can occur even when o 0, within a limited region of size increasing with the value of o. The quantum mechanical extension of this method allows applications for the nanodiffusion in nanostructured, porous and cellular materials, as for biological, medical and nanopiezotronic devices.
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