Ultrametric Cantor sets and Origin of Anomalous Diffusion
arXiv:1008.2366
Abstract
The anomalous mean square fluctuations are shown to arise naturally from the ordinary diffusion equation interpreted scale invariantly in a formalism endowing real numbers with a nonarchimedean multiplicative structure. A variable approaching 0 linearly in the ordinary analysis is shown to enjoy instead a sublinear flow in the presence of this scale invariant structure. Diffusion on an ultrametric Cantor set is also generically subdiffusive with the above sublinear mean square deviation. The present study seems to offer a new interpretation of a possible emergence of complex patterns from an apparently simple system.
Latex 2e, 12 pages