Journal article

Publication year: 1995

Pages: 53-56

Journal: Physical Review E

Volume number: 52

Issue number: 1

ISSN: 1539-3755

DOI Link: https://doi.org/10.1103/PhysRevE.52.53

Publisher: American Physical Society

Abstract: 
We find that the relevant quantities describing the localization of electrons, vibrations, and random walks on random fractals are non-self-averaging. There exists a crossover distance r(x) that increases logarithmically with the number N of configurations considered in the averages. For vibrations and electrons, the localization exponent changes from 1 below r(x) to d(min) above r(x). For random walks, the exponent changes from d(u)/(d(u) - 1) to d(min)d(w)/(d(w)-d(min)), where d(w) and d(min) are the fractal dimensions of the random walk and the shortest path on the fractal, respectively. Our results explain the controversies regarding the localization exponent.

Harvard Citation style: Bunde, A. and Dräger, J. (1995) Localization in disordered structures: Breakdown of the self-averaging hypothesis, Physical Review E, 52(1), pp. 53-56. https://doi.org/10.1103/PhysRevE.52.53

APA Citation style: Bunde, A., & Dräger, J. (1995). Localization in disordered structures: Breakdown of the self-averaging hypothesis. Physical Review E. 52(1), 53-56. https://doi.org/10.1103/PhysRevE.52.53