Abstract
The Cole-Cole behaviour of the complex susceptibility is derived from the diffusion limit of a random walk of permanent dipoles that is the discrete orientation model with a Levy like distribution of waiting times at the sites. The method yields a generalisation of the Smoluchowski equation of the classical theory of the Brownian motion in a potential which describes the behaviour of the distribution function in configuration space with a fixed waiting time to a system which exhibits chaotic behaviour of the waiting times. It is indicated how the fundamental solution of the Smoluchowski equation in the absence of a potential may be obtained as a Levy distribution by simply using the properties of the characteristic function which is the Mittag-Leffler function. Such a representation also yields in a simple manner both the mean square displacement of a dipole and the after effect function of the Cole-Cole process.
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