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

Description

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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