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14 December 2024
 
  » arxiv » cond-mat/9710273

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Cutting-Decimation Renormalization for diffusive and vibrational dynamics on fractals
Raffaella Burioni ; Davide Cassi ; Sofia Regina ;
Date 24 Oct 1997
Subject Statistical Mechanics | cond-mat.stat-mech
AbstractRecently, 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.
Source arXiv, cond-mat/9710273
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