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Local and average behaviour in inhomogeneous superdiffusive media (Articolo in rivista)

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Local and average behaviour in inhomogeneous superdiffusive media (Articolo in rivista) (literal)

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Alessandro Vezzani (a,b); Raffaella Burioni (b,c); Luca Caniparoli (d); Stefano Lepri (e) (2011)
Local and average behaviour in inhomogeneous superdiffusive media
in Philosophical magazine (2003, Print)
(literal)

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Alessandro Vezzani (a,b); Raffaella Burioni (b,c); Luca Caniparoli (d); Stefano Lepri (e) (literal)

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Special Issue: Twelfth International Workshop on Complex Systems: Andalo (Trento) Italy. 15-18 March 2010 (literal)

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a) Centro S3, CNR-Istituto di Nanoscienze, via Campi 213A, 41125 Modena, Italy b) Dipartimento di Fisica, Università degli Studi di Parma, viale G.P. Usberti 7/A, 43100 Parma, Italy c) INFN, Gruppo Collegato di Parma, viale G.P. Usberti 7/A, 43100 Parma, Italy d) International School for Advanced Studies SISSA, via Beirut 2/4, 34151, Trieste, Italy e) Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy (literal)

Titolo

Abstract

We consider a random walk on one-dimensional inhomogeneous graphs built from Cantor fractals. Our study is motivated by recent experiments that demonstrated superdiffusion of light in complex disordered materials, thereby termed Lévy glasses. We introduce a geometric parameter ? which plays a role analogous to the exponent characterising the step length distribution in random systems. We study the large-time behaviour of both local and average observables; for the latter case, we distinguish two different types of averages, respectively over the set of all initial sites and over the scattering sites only. The \"single long-jump approximation\" is applied to analytically determine the different asymptotic behaviour as a function of ? and to understand their origin. We also discuss the possibility that the root of the mean square displacement and the characteristic length of the walker distribution may grow according to different power laws; this anomalous behaviour is typical of processes characterised by Lévy statistics and here, in particular, it is shown to influence average quantities. (literal)

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