Anomalous Diffusion and Fractons in Disordered Structures

摘要: In this lecture I review the developments of recent years in our understanding transport properties disordered structures. The breakthrough area came about largely by discovery anomalous diffusion1–4 and concept fractons introduced Alexander Orbach.1 These are based on fundamental fractals developed Mandelbrot5 to characterize structures nature. Since then (1982), interest scientific community has increased dramatically, as a consequence hundreds papers have been published subject. existence diffusion for case singular transition rates regular lattices was known earlier (see e.g., articles et al6 Weiss Rubin7). fact that disorder lattice structure can lead anomalies surprising result presented Refs.1–4. Although today there is much better dynamical structures, still remain many open questions, static well not fully understood. will focus several basic such conductivity, fractons. also discuss chemical distance probability density random walks which contain information properties. Relevant experiments be mentioned only briefly since they discussed detail talks Jorgen Kjems Eric Courtens. Effects additional physical different from structural talk Armin Bunde.