Diffusion and spectral dimension on Eden tree

Hisao Nakanishi; Hans J. Herrmann

doi:10.1088/0305-4470/26/18/018

Diffusion and spectral dimension on Eden tree

凝聚态物理 2009-10-22 v1

作者: Hisao Nakanishi , Hans J. Herrmann

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摘要

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.

关键词

random walk theory

引用

@article{arxiv.cond-mat/9211020,
  title  = {Diffusion and spectral dimension on Eden tree},
  author = {Hisao Nakanishi and Hans J. Herrmann},
  journal= {arXiv preprint arXiv:cond-mat/9211020},
  year   = {2009}
}

备注

11 pages, Plain TeX with J-Phys.sty style, HLRZ 93/92

Diffusion and spectral dimension on Eden tree

摘要

关键词

引用

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