Diffusion and spectral dimension on Eden tree
Abstract
We calculate the eigenspectrum of random walks on the Eden tree in two and three dimensions. From this, we calculate the spectral dimension ds and the walk dimension dw and test the scaling relation ds = 2df/dw (=2d/dw 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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