A fractal description of the dielectric response of disordered materials

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Abstract
The author uses a generalized diffusion equation to derive theories for the dielectric response of materials exhibiting fractal dynamics. Earlier results for the relaxation of charge carriers on fractal aggregates and fractal surfaces, as well as by fractal time processes, are obtained by simple scaling arguments. It is argued that the existence of cut-offs to the fractal structures and processes leads to dielectric response functions of the Cole-Cole form for bound charge carriers and of the Davidson-Cole form for quasi-free charge carriers. A novel expression is proposed for the case of a convolution of two fractal processes. These response functions are compared with other theoretical treatments and their relevance for experiments is assessed.