Lévy flights and multifractality in quantum critical diffusion and in classical random walks on fractals

We employ the method of virial expansion to compute the retarded density correlation function (generalized diffusion propagator) in the critical random matrix ensemble in the limit of strong multifractality. We find that the long-range nature of the Hamiltonian is a common root of both multifractali...

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Published inPhysical review. E, Statistical, nonlinear, and soft matter physics Vol. 86; no. 2 Pt 1; p. 021136
Main Authors Kravtsov, V E, Yevtushenko, O M, Snajberk, P, Cuevas, E
Format Journal Article
LanguageEnglish
Published United States 01.08.2012
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Summary:We employ the method of virial expansion to compute the retarded density correlation function (generalized diffusion propagator) in the critical random matrix ensemble in the limit of strong multifractality. We find that the long-range nature of the Hamiltonian is a common root of both multifractality and Lévy flights, which show up in the power-law intermediate- and long-distance behaviors, respectively, of the density correlation function. We review certain models of classical random walks on fractals and show the similarity of the density correlation function in them to that for the quantum problem described by the random critical long-range Hamiltonians.
ISSN:1550-2376
DOI:10.1103/PhysRevE.86.021136