Vibrational excitations in percolation: Localization and multifractality | Zendy

Armin Bunde | Zendy; H. Eduardo Roman | Zendy; Stefanie Russ | Zendy; Am Aharony | Zendy; A. B. Harris | Zendy

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Vibrational excitations in percolation: Localization and multifractality

Author(s) -

Armin Bunde,

H. Eduardo Roman,

Stefanie Russ,

Am Aharony,

A. B. Harris

Publication year - 1992

Publication title -

physical review letters

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.688

H-Index - 673

eISSN - 1079-7114

pISSN - 0031-9007

DOI - 10.1103/physrevlett.69.3189

Subject(s) - percolation (cognitive psychology) , physics , multifractal system , percolation theory , generalization , distribution (mathematics) , euclidean geometry , exponential function , statistical physics , cluster (spacecraft) , amplitude , distribution function , percolation threshold , combinatorics , quantum mechanics , fractal , mathematical analysis , mathematics , geometry , electrical resistivity and conductivity , computer science , conductivity , programming language , neuroscience , biology

We discuss localized excitations on the incipient infintie percolation cluster. Assuming a simple exponential decay of the amplitudes Ψ i 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 movements of Ψ i exhibit novel corssover phenomena. Our numerical simulations of fractons exhibit a nontrivial distribution of localization lengths, even when the chemical distance is fixed

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