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Diffusion and spectral dimension on Eden tree

Hisao Nakanishi·Hans J. Herrmann
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Abstract

We calculate the eigenspectrum of random walks on the Eden tree in two and three dimensions. From this, we calculate the spectral dimension $d_s$ and the walk dimension $d_w$ and test the scaling relation $d_s = 2d_f/d_w$ ($=2d/d_w$ for an Eden tree). Finite-size induced crossovers are observed, whereby the system crosses over from a short-time regime where this relation is violated (particularly in two dimensions) to a long-time regime where the behavior appears to be complicated and dependent on dimension even qualitatively.

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Hisao Nakanishi, Hans J. Herrmann. 1992-11-27. Diffusion and spectral dimension on Eden tree. https://doi.org/10.1088/0305-4470%2F26%2F18%2F018

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