Frequency-dependent conductivity in glasses

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Abstract
The Barton-Nakajima-Namikawa relationship between the static dielectric constant epsilon (0), and the DC conductivity sigma (0), observed in many glasses, sigma (0) varies as omega c epsilon (0), with omega c the loss peak frequency, has been generally assumed to signify a connection between the low frequency AC and the DC conduction processes. The author argues that the connection is that both are due to non-local relaxation processes, the relaxation time of the DC process being effectively infinite. Above the loss peak, the relation sigma ( omega ) varies as omega s is compatible with the pair approximation, i.e. a local relaxation theory. Below the loss peak, the role of Coulomb interactions is critical. If the effects of Coulomb interactions may be neglected, or treated perturbatively, the relaxation time of a process spanning a linear dimension x is proportional to x2. But if Coulomb interactions dominate, the relaxation time may be proportional to x. Only the latter condition is compatible with the BNN relation, and is believed to be one of the most important distinctions between the ionic glasses and the Fermi (electronic) glass.