Regensburg 2010 – wissenschaftliches Programm
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BP: Fachverband Biologische Physik
BP 18: Anomalous Transport II (joint BP, DY)
BP 18.3: Vortrag
Mittwoch, 24. März 2010, 11:45–12:00, H38
Random walks on d-dimensional Sierpinski gaskets: Asymptotics, DSI, and Puzzles — •Sebastian Weber1, Joseph Klafter2,1, and Alexander Blumen3 — 1Freiburg Institute For Advanced Studies (FRIAS), University of Freiburg, Germany — 2School of Chemistry, Tel Aviv University, Israel — 3Theoretical Polymer Physics, University of Freiburg, Germany
We study the effect of the embedding dimension d of a random walk (RW) taking place on a d-dimensional Sierpinski gasket fractal in its classical and dual versions. In the limit of large d the spectral dimension ds approaches 2 such that the RW dynamics, which is governed by the ds, is expected to behave similarly to a RW on a 2 dimensional lattice. In sharp contrast to that, we observe much richer characteristics for the RW. First, the time discrete scale invariance (DSI) phenomena cause log-periodic oscillations, which increase in amplitude for larger d. Second, the asymptotic approach to theoretically predicted power-laws of standard RW observables is significantly altered, depending on the variant of the Sierpinski gasket used (classical or dual) and on d. Furthermore, we address the suitability of standard RW observables to determine the spectral dimension ds. This analysis is of great practical relevance and shows unexpected, puzzling results.