Cutting-Decimation Renormalization for diffusive and vibrational dynamics on fractals

Details Cutting-Decimation Renormalization for diffusive and vibrational dynamics on fractals Cutting-Decimation Renormalization for diffusive and vibrational dynamics on fractals

1997-10-24

arxiv.org/abs/cond-mat/9710273v1

Physics

Condensed Matter

Statistical Mechanics

10 pages Latex, 3 figures (figures are postscript files)

Scientific paper

Recently, we pointed out that on a class on non exactly decimable fractals two different parameters are required to describe diffusive and vibrational dynamics. This phenomenon we call dynamical dimension splitting is related to the lack of exact decimation invariance for these structures, which turn out to be invariant under a more complex cutting-decimation transform. In this paper we study in details the dynamical dimension splitting on these fractals analyzing the mathematical properties of the cutting-decimation transform. Our results clarify how the splitting arises from the cutting transform and show that the dynamical dimension degeneration is a very peculiar consequence of exact decimability.

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