Markov chain analysis of random walks on disordered medium

Дата и время публикации : 1993-11-12T14:09:13Z

Авторы публикации и институты :
Sonali Mukherjee
Hisao Nakanishi
Norman H. Fuchs

Ссылка на журнал-издание: Ссылка на журнал-издание не найдена
Коментарии к cтатье: 34 pages, REVTEX 3.0
Первичная категория: cond-mat

Все категории : cond-mat

Краткий обзор статьи: We study the dynamical exponents $d_{w}$ and $d_{s}$ for a particle diffusing in a disordered medium (modeled by a percolation cluster), from the regime of extreme disorder (i.e., when the percolation cluster is a fractal at $p=p_{c}$) to the Lorentz gas regime when the cluster has weak disorder at $p>p_{c}$ and the leading behavior is standard diffusion. A new technique of relating the velocity autocorrelation function and the return to the starting point probability to the asymptotic spectral properties of the hopping transition probability matrix of the diffusing particle is used, and the latter is numerically analyzed using the Arnoldi-Saad algorithm. We also present evidence for a new scaling relation for the second largest eigenvalue in terms of the size of the cluster, $|ln{lambda}_{max}|sim S^{-d_w/d_f}$, which provides a very efficient and accurate method of extracting the spectral dimension $d_s$ where $d_s=2d_f/d_w$.

Category: Physics