Journalartikel

Jahr der Veröffentlichung: 1995

Seiten: 53-56

Zeitschrift: Physical Review E

Bandnummer: 52

Heftnummer: 1

ISSN: 1539-3755

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

Verlag: 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-Zitierstil: 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-Zitierstil: 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