Diffusion, localization and dispersion relations on ``small-world'' lattices
无序系统与神经网络
2009-10-31 v1
摘要
The spectral properties of the Laplacian operator on ``small-world'' lattices, that is mixtures of unidimensional chains and random graphs structures are investigated numerically and analytically. A transfer matrix formalism including a self-consistent potential a la Edwards is introduced. In the extended region of the spectrum, an effective medium calculation provides the density of states and pseudo relations of dispersion for the eigenmodes in close agreement with the simulations. Localization effects, which are due to connectivity fluctuations of the sites are shown to be quantitatively described by the single defect approximation recently introduced for random graphs.
引用
@article{arxiv.cond-mat/9903347,
title = {Diffusion, localization and dispersion relations on ``small-world'' lattices},
author = {Remi Monasson},
journal= {arXiv preprint arXiv:cond-mat/9903347},
year = {2009}
}
备注
17 revtex pages, 16 eps figures + 2 tables