Date of this Version
Physical Review Letters
We discuss localized excitations on the incipient infinite percolation cluster. Assuming a simple exponential decay of the amplitudes ψi in terms of the chemical (minimal) path, we show theoretically that the ψ’s are characterized by a logarithmically broad distribution, and display multifractal features as a function of the Euclidean distance. The moments of ψi exhibit novel crossover phenomena. Our numerical simulations of fractons exhibit a nontrivial distribution of localization lengths, even when the chemical distance is fixed. These results are explained via a generalization of the theory.
Bunde, A., Roman, H., Russ, S., Aharony, A., & Harris, A. (1992). Vibrational Excitations in Percolation: Localization and Multifractality. Physical Review Letters, 69 (22), 3189-3192. http://dx.doi.org/10.1103/PhysRevLett.69.3189
Date Posted: 20 August 2015
This document has been peer reviewed.