DYNAMICAL PROPERTIES OF FRACTAL NETWORKS - SCALING, NUMERICAL SIMULATIONS, AND PHYSICAL REALIZATIONS

This article describes the advances that have been made over the past ten years on the problem of fracton excitations in fractal structures. The relevant systems to this subject are so numerous that focus is li mited to a specific structure, the percolating network. Recent progres s has followed three directions: scaling, numerical simulations, and e xperiment. In a happy coincidence, large-scale computations, especiall y those involving array processors, have become possible in recent yea rs. Experimental techniques such as light- and neutron-scattering expe riments have also been developed. Together, they form the basis for a review article useful as a guide to understanding these developments a nd for charting future research directions. In addition, new numerical simulation results for the dynamical properties of diluted antiferrom agnets are presented and interpreted in terms of scaling arguments. Th e authors hope this article will bring the major advances and future i ssues facing this field into clearer focus, and will stimulate further research on the dynamical properties of random systems.