Fluctuation theory of relaxation phenomena in disordered conductors: How fitting laws such as those of Kohlrausch and Jonscher are obtained from a consistent approach

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Abstract
A theoretical approach to the description of temporal and frequency responses of glasslike conductors is developed and a detailed mathematical analysis of response functions is given. Being derived from general principles of Gaussian statistics of Coulomb fluctuations, which are produced by the random field of charged defects, these functions can be expressed in terms of the initial conductivity (without disorder) and a fluctuation exponent that reflects the sensitivity of mobile charges to disorder. In light of our present results, the Gaussian model of the distribution of activation barriers in glasslike systems is put on firm theoretical ground. The derived conductivity of the disordered medium reproduces all characteristic features of the empirical Jonscher law; also, the frequency range where it can be observed increases exponentially with the fluctuation exponent. The latter determines both the Jonscher exponent and the fractional exponent in the so-called Kohlrausch law. In this case, the non-Debye relaxation time takes the strict Arrhenius form with the effective activation energy carrying information about the disorder. The obtained results are compared with experimental data and possible ways to reconcile the discrepancy between theory and experiment are discussed. © 1996 The American Physical Society.