FLUCTUATION THEORY OF RELAXATION PHENOMENA IN DISORDERED CONDUCTORS -HOW FITTING LAWS SUCH AS THOSE OF KOHLRAUSCH AND JONSCHER ARE OBTAINED FROM A CONSISTENT APPROACH

A theoretical approach to the description of temporal and frequency re sponses of glasslike conductors is developed and a detailed mathematic al analysis of response functions is given. Being derived from general principles of Gaussian statistics of Coulomb fluctuations, which art produced by the random field of charged defects. these functions can b e expressed in terms of the initial conductivity (without disorder) an d a fluctuation exponent that reflects the sensitivity of mobile charg es to disorder. In light of our present results, the Gaussian model of the distribution of activation barriers in glasslike systems is put o n firm theoretical ground, The derived conductivity of the disordered medium reproduces all characteristic features of the empirical Jonsche r law; also, the frequency range where it can be observed increases ex ponentially with the fluctuation exponent. The latter determines both the Jonscher exponent and the fractional exponent in the so-called Koh lrausch law. In this case, the non-Debye relaxation time Lakes the str ict Arrhenius form with the effective activation energy carrying infor mation about the disorder. The obtained results are compared with expe rimental data and possible ways to reconcile the discrepancy between t heory and experiment are discussed.