Journal article

Authors list: Kantelhardt, JW; Bunde, A

Publication year: 1997

Pages: 6693-6701

Journal: Physical Review E

Volume number: 56

Issue number: 6

ISSN: 1063-651X

DOI Link: https://doi.org/10.1103/PhysRevE.56.6693

Publisher: American Physical Society

Abstract: 
We discuss the localization of electronic eigenfunctions and vibrational excitations ("fractons") on selfsimilar percolation clusters at criticality on the Cayley tree, in d = 2, and in d = 3, both in topological (l) and in Euclidian (r) space. We find that the localization behavior of electrons and fractons is very similar, but does depend on the type of average performed and on the number of configurations N taken into account. It can be characterized by three different localization regimes. In the first regime, at small distances l and r from the localization center, electrons and fractons are superlocalized in d space, while the localization is not exponential in r space. In the intermediate regime, which is the most important one, we find stretched exponential localization ("sublocalization"), In[psi]similar to-l(d psi,l) or similar to-r(d psi,r) with effective localization exponents d(psi,l) approximate to d(psi,r) approximate to 0.6. In the third regime, for large l and r, the averages strongly depend on the number of configurations, even in l space, and superlocalization (d(psi,l), d(psi,r) >1) is observed, converging to simple exponential behavior asymptotically. To understand this complicated localization behavior, we present an analytical calculation of In[psi] for the third regime, which is based on the fact that the local amplitudes at large distances from the localization center obey a log-normal distribution.

Harvard Citation style: Kantelhardt, J. and Bunde, A. (1997) Electrons and fractons on percolation structures at criticality: Sublocalization and superlocalization, PHYSICAL REVIEW E, 56(6), pp. 6693-6701. https://doi.org/10.1103/PhysRevE.56.6693

APA Citation style: Kantelhardt, J., & Bunde, A. (1997). Electrons and fractons on percolation structures at criticality: Sublocalization and superlocalization. PHYSICAL REVIEW E. 56(6), 6693-6701. https://doi.org/10.1103/PhysRevE.56.6693