Random Fluctuations and Pattern Growth: Experiments and Models (NATO Science Series E: (closed)) (0792300726)

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Random Fluctuations and Pattern Growth: "Experiments and Models" (NATO Science Series E: (closed))

In this lecture I review the developments of recent years in our understanding of trans-

transport properties in disordered structures. The breakthrough in this area came about

largely by the discovery of anomalous diffusion and by the concept of fractons

introduced by Alexander and Orbach. These are based on the fundamental

concept of fractals introduced and developed by Mandelbrot to characterize disordered

structures in nature.

Since then the interest of the scientific community in

this area has increased dramatically, and as a consequence hundreds of papers have

been published on this subject. The existence of anomalous diffusion for the case of

singular transition rates on regular lattices was known earlier (see e.g., the review

articles of Alexander et al and Weiss and Rubin). The fact that disorder in the

lattice structure can lead to anomalies in the transport properties was the surprising

result presented in Refis. Although today there is a much better understanding

of the dynamical properties of disordered structures, there still remain many open

questions, and the static properties as well as the dynamical properties are not fully

understood. In this lecture I will focus on several basic dynamical properties such

as conductivity, diffusion and fractons. I will also discuss the concept of chemical

distance and the probability density of random walks on fractals which contain much

information about the dynamical properties. Relevant experiments will be mentioned

only briefly since they will be discussed in detail in the talks of Jorgen Kjems and

Eric Courtens. Effects of additional physical disorder which are different from the

structural disorder will be discussed in the talk of Armin Bunde.

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