Vibrational excitations in percolation: Localization and multifractality

Armin Bunde*, H. Eduardo Roman, Stefanie Russ, Amnon Aharony, A. Brooks Harris

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


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.

Original languageEnglish
Pages (from-to)3189-3192
Number of pages4
JournalPhysical Review Letters
Issue number22
StatePublished - 1992


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