Universal behavior of anomalous ionic conductivity - Relaxation mode theory

On the basis of the relaxation mode theory in a noninteracting lattice gas, the anomalous dynamic conductivity Re sigma(omega) = sigma(0) + A omega(s) + A'omega(s'), s approximate to 0.6, s' approximate to 1 is fully examined in a random supercell system having a uniform distribution of the activation energies U-min less than or equal to U less than or equal to U-max; the low-frequency and high-temperature region A omega(s) is governed py the extended nondiffusive modes, while the high-frequency and low-temperature region A'omega(s') is regulated by the localized nondiffusive modes. The dynamical crossover exists in-between. The frequency power s is almost independent of temperature but s' changes with it. The coefficient approximately given by A approximate to beta exp {-beta(1- s)U-max} shows a strong temperature dependence since s approximate to 0.6, and A' approximate to beta exp{-beta(1- s')U-min} depends but weakly on temperature because s' approximate to 1. All these characteristics, which are quite consistent with the experiments of Nowick et al., are originated is regulated by the localized in a single mechanism of the mode diffusion length L-epsilon approximate to T-epsilon(alpha/2) and density of states D-epsilon approximate to tau(epsilon)(delta) where tau(epsilon) is the mode relaxation time.