An exact renormalization group describes extremely slow, logarithmic diffusion in the presence of a biasing field on ramified fractal structures. Recursion equations are singular at the fixed point and the standard analysis to extract asymptotic behaviors has to be reconsidered. The model reproduces mechanisms working for biased diffusion on percolation clusters. For 1 - d structures, logarithmic diffusions generalizing that discussed by Sinai [Theory Probab. Its Appl. 27, 256 (1982)] are obtained by the same methods.
Singular Dynamical Renormalization-group and Biased Diffusion On Fractals
MARITAN, AMOS;STELLA, ATTILIO
1993
Abstract
An exact renormalization group describes extremely slow, logarithmic diffusion in the presence of a biasing field on ramified fractal structures. Recursion equations are singular at the fixed point and the standard analysis to extract asymptotic behaviors has to be reconsidered. The model reproduces mechanisms working for biased diffusion on percolation clusters. For 1 - d structures, logarithmic diffusions generalizing that discussed by Sinai [Theory Probab. Its Appl. 27, 256 (1982)] are obtained by the same methods.File in questo prodotto:
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